Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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 | #123×C37 | C2 |
| hypercenter | #123 | D37 |
| hypocenter | C37 | #547 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10596962 | C2 | semidirect |
| 2. C2×#10596964 | C2 | semidirect |
| 3. #11924535 | C2 | semidirect |
| 4. #11924521 | C2 | semidirect |
| 5. #11924520 | C2 | semidirect |
| 6. #11924518 | C2 | semidirect |
| 7. #11924514 | C2 | semidirect |
| 8. #11924513 | C2 | semidirect |
| 9. #11924509 | C2 | semidirect |
| 10. #11924508 | C2 | semidirect |
| 11. #11924496 | C2 | semidirect |
| 12. #11924496 | C2 | semidirect |
| 13. C2×#10596936 | C2 | semidirect |
| 14. C4⋊C4×D37 | C2 | semidirect |
| 15. #123×C37 | C2 | semidirect |
| 67. C22⋊D37 | D4 | semidirect |
| 107. Dic37 | #41 | semidirect |
| 116. C37 | #547 | semidirect |
| 123. #123 | D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10596962 | 2 |
| C2×#10596964 | 2 |
| #11924535 | 2 |
| #11924521 | 2 |
| #11924520 | 2 |
| #11924518 | 2 |
| #11924514 | 2 |
| #11924513 | 2 |
| #11924509 | 2 |
| #11924508 | 2 |
| #11924496 | 2 |
| C2×#10596936 | 2 |
| C4⋊C4×D37 | 2 |
| #123×C37 | 2 |
| #547 | 37 |