Finite Group DatabasebetaFinite Group DatabasebetaOrder 22976.
252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D359 |
| commutator, socle, cosocle | C22×C359 | C24 |
| Fitting | #123×C359 | C2 |
| hypercenter | #123 | D359 |
| hypocenter | C359 | #560 |
| LCS | G ▷ C22×C359 ▷ C359 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26040011 | C2 | semidirect |
| 2. #26040010 | C2 | semidirect |
| 3. #26039997 | C2 | semidirect |
| 4. #26039990 | C2 | semidirect |
| 5. #26039989 | C2 | semidirect |
| 6. #26039988 | C2 | semidirect |
| 7. #26039985 | C2 | semidirect |
| 8. #26039983 | C2 | semidirect |
| 9. #123×C359 | C2 | semidirect |
| 13. C2×D1436 | C22 | semidirect |
| 16. C2×C22⋊D359 | C22 | semidirect |
| 17. C2×C4×D359 | C22 | semidirect |
| 18. C4⋊Dic359 | C22 | semidirect |
| 19. Dic359⋊C4 | C22 | semidirect |
| 24. (C2×D359)⋊C4 | C22 | semidirect |
| 25. C4×Dic359 | C22 | semidirect |
| 27. C22×C4×C359 | C22 | semidirect |
| 28. C4⋊C4×C359 | C22 | semidirect |
| 30. C22⋊C4×C359 | C22 | semidirect |
| 74. C359 | #560 | semidirect |
| 79. #123 | D359 | semidirect |
| 94. C22×C4 | C2×D359 | semidirect |
| 97. C4⋊C4 | C2×D359 | semidirect |
| 104. C22⋊C4 | C2×D359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26040011 | 2 |
| #26040010 | 2 |
| #26039997 | 2 |
| #26039990 | 2 |
| #26039989 | 2 |
| #26039988 | 2 |
| #26039985 | 2 |
| #26039983 | 2 |
| #123×C359 | 2 |
| #560 | 359 |