Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
238 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 99 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 | C4×D4×C37 | C2 |
| hypercenter | C4×D4 | D37 |
| hypocenter | C37 | #553 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11924531 | C2 | semidirect |
| 2. #11924528 | C2 | semidirect |
| 3. #11924518 | C2 | semidirect |
| 4. #11924510 | C2 | semidirect |
| 5. #11924510 | C2 | semidirect |
| 6. #11924508 | C2 | semidirect |
| 7. C4×D148 | C2 | semidirect |
| 8. #11924496 | C2 | semidirect |
| 9. #11924495 | C2 | semidirect |
| 10. C2×C4⋊Dic37 | C2 | semidirect |
| 11. C4×D4×C37 | C2 | semidirect |
| 79. C37 | #553 | semidirect |
| 88. C4×D4 | D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11924531 | 2 |
| #11924528 | 2 |
| #11924518 | 2 |
| #11924510 | 2 |
| #11924508 | 2 |
| C4×D148 | 2 |
| #11924496 | 2 |
| #11924495 | 2 |
| C2×C4⋊Dic37 | 2 |
| C4×D4×C37 | 2 |
| #553 | 37 |