Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
284 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 148 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8×C181 | C22⋊C4 |
| commutator | C22 | C2×C42×C181 |
| Frattini, cosocle | C22×C4 | C23×C181 |
| socle | C2×C181 | C4×C22⋊C4 |
| prime radical | C2×#41×C181 | C22 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C181 ◁ C22×C8×C181 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #405×C181 | C2 | semidirect |
| 5. #344×C181 | C2 | semidirect |
| 9. C2×M16×C181 | C4 | semidirect |
| 12. C22×C8×C181 | C4 | semidirect |
| 15. #101×C181 | C4 | semidirect |
| 16. #100×C181 | C4 | semidirect |
| 74. C181 | #1757 | direct (N × H) |
| 75. #1757 | C181 | direct (N × H) |
| 79. #405 | C2×C181 | semidirect |
| 80. #344 | C2×C181 | semidirect |
| 84. C2×M16 | C4×C181 | semidirect |
| 87. C22×C8 | C4×C181 | semidirect |
| 90. #101 | C4×C181 | semidirect |
| 91. #100 | C4×C181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#131×C181 | 2 |
| #413×C181 | 2 |
| #410×C181 | 2 |
| #405×C181 | 2 |
| #344×C181 | 2 |
| #1757 | 181 |