Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
520 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 188 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C181 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C181 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C181 ◁ C23×C4×C181 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#121×C181 | C2 | semidirect |
| 2. #480×C181 | C2 | semidirect |
| 3. #466×C181 | C2 | semidirect |
| 4. #447×C181 | C2 | semidirect |
| 5. C2×C22⋊C8×C181 | C2 | semidirect |
| 7. C22×D4×C181 | C22 | semidirect |
| 9. C2×D8×C181 | C22 | semidirect |
| 10. C22×C8×C181 | C22 | semidirect |
| 14. #121×C181 | C22 | semidirect |
| 15. C2×C4⋊C4×C181 | C22 | semidirect |
| 17. #107×C181 | C22 | semidirect |
| 18. #102×C181 | C22 | semidirect |
| 19. C22⋊C8×C181 | C22 | semidirect |
| 47. C23×C181 | D8 | semidirect |
| 86. C181 | #3186 | direct (N × H) |
| 87. #3186 | C181 | direct (N × H) |
| 88. C2×#121 | C2×C181 | semidirect |
| 89. #480 | C2×C181 | semidirect |
| 90. #466 | C2×C181 | semidirect |
| 91. #447 | C2×C181 | semidirect |
| 92. C2×C22⋊C8 | C2×C181 | semidirect |
| 94. C22×D4 | C22×C181 | semidirect |
| 96. C2×D8 | C22×C181 | semidirect |
| 97. C22×C8 | C22×C181 | semidirect |
| 101. #121 | C22×C181 | semidirect |
| 102. C2×C4⋊C4 | C22×C181 | semidirect |
| 104. #107 | C22×C181 | semidirect |
| 105. #102 | C22×C181 | semidirect |
| 106. C22⋊C8 | C22×C181 | semidirect |
| 134. C23 | D8×C181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#121×C181 | 2 |
| #480×C181 | 2 |
| #466×C181 | 2 |
| #447×C181 | 2 |
| C2×C22⋊C8×C181 | 2 |
| #3186 | 181 |