Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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 | #124×C37 | C2 |
| prime radical | #11924508 | C2 |
| hypercenter | #124 | D37 |
| hypocenter | C37 | #542 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11924534 | C2 | semidirect |
| 2. #11924530 | C2 | semidirect |
| 3. #11924529 | C2 | semidirect |
| 4. #11924522 | C2 | semidirect |
| 5. #11924522 | C2 | semidirect |
| 6. #11924518 | C2 | semidirect |
| 7. #11924517 | C2 | semidirect |
| 8. #11924513 | C2 | semidirect |
| 9. #11924513 | C2 | semidirect |
| 10. #11924512 | C2 | semidirect |
| 12. C4×Dic74 | C2 | semidirect |
| 13. #11924496 | C2 | semidirect |
| 14. #11924492 | C2 | semidirect |
| 15. #124×C37 | C2 | semidirect |
| 104. C37 | #542 | semidirect |
| 110. #124 | D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11924534 | 2 |
| #11924530 | 2 |
| #11924529 | 2 |
| #11924522 | 2 |
| #11924518 | 2 |
| #11924517 | 2 |
| #11924513 | 2 |
| #11924512 | 2 |
| #11924508 | 2 |
| C4×Dic74 | 2 |
| #11924496 | 2 |
| #11924492 | 2 |
| #124×C37 | 2 |
| #542 | 37 |