Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
238 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 97 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 | #125×C37 | C2 |
| hypercenter | #125 | D37 |
| hypocenter | C37 | #553 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ #125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11924531 | C2 | semidirect |
| 2. #11924521 | C2 | semidirect |
| 3. #11924511 | C2 | semidirect |
| 4. #11924511 | C2 | semidirect |
| 5. #11924511 | C2 | semidirect |
| 6. C4×D148 | C2 | semidirect |
| 7. C4×D148 | C2 | semidirect |
| 8. #11924498 | C2 | semidirect |
| 9. #11924494 | C2 | semidirect |
| 10. C4⋊C4×D37 | C2 | semidirect |
| 11. #125×C37 | C2 | semidirect |
| 79. C37 | #553 | semidirect |
| 81. #125 | D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11924531 | 2 |
| #11924521 | 2 |
| #11924511 | 2 |
| C4×D148 | 2 |
| #11924498 | 2 |
| #11924494 | 2 |
| C4⋊C4×D37 | 2 |
| #125×C37 | 2 |
| #553 | 37 |