Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
484 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 192 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×C23 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C23 |
| prime radical | C2×C23×#127 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C2×C42×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#533 | C2 | semidirect |
| 3. C23×#490 | C2 | semidirect |
| 4. C23×#486 | C2 | semidirect |
| 5. C23×#418 | C2 | semidirect |
| 6. C4×M16×C23 | C2 | semidirect |
| 10. C23×C4⋊Q8 | C22 | semidirect |
| 14. C23×#125 | C22 | semidirect |
| 19. C23×#102 | C22 | semidirect |
| 20. C23×#97 | C22 | semidirect |
| 21. C4×C8×C23 | C22 | semidirect |
| 59. #3138 | C23 | direct (N × H) |
| 71. #533 | C2×C23 | semidirect |
| 73. #490 | C2×C23 | semidirect |
| 74. #486 | C2×C23 | semidirect |
| 75. #418 | C2×C23 | semidirect |
| 76. C4×M16 | C2×C23 | semidirect |
| 84. C4⋊Q8 | C22×C23 | semidirect |
| 88. #125 | C22×C23 | semidirect |
| 93. #102 | C22×C23 | semidirect |
| 94. #97 | C22×C23 | semidirect |
| 95. C4×C8 | C22×C23 | semidirect |
| 96. C23 | #3138 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#533 | 2 |
| C2×C23×#127 | 2 |
| C23×#490 | 2 |
| C23×#486 | 2 |
| C23×#418 | 2 |
| C4×M16×C23 | 2 |
| #3138 | 23 |