Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
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×D37 |
| commutator, socle, cosocle | C22×C37 | C24 |
| Fitting | #126×C37 | C2 |
| hypercenter | #126 | D37 |
| hypocenter | C37 | #560 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11924533 | C2 | semidirect |
| 2. #11924530 | C2 | semidirect |
| 3. #11924521 | C2 | semidirect |
| 4. #11924511 | C2 | semidirect |
| 5. #11924509 | C2 | semidirect |
| 6. #11924506 | C2 | semidirect |
| 7. #126×C37 | C2 | semidirect |
| 12. C2×D148 | C22 | semidirect |
| 13. C2×C4×D37 | C22 | semidirect |
| 14. C4⋊C4×C37 | C22 | semidirect |
| 16. C42×C37 | C22 | semidirect |
| 19. #10596938 | C22 | semidirect |
| 20. #10596936 | C22 | semidirect |
| 51. C37 | #560 | semidirect |
| 54. #126 | D37 | semidirect |
| 66. C4⋊C4 | C2×D37 | semidirect |
| 71. C42 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11924533 | 2 |
| #11924530 | 2 |
| #11924521 | 2 |
| #11924511 | 2 |
| #11924509 | 2 |
| #11924506 | 2 |
| #126×C37 | 2 |
| #560 | 37 |