Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 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 | C2 | C2×D4×D37 |
| commutator, cosocle | C4×C37 | C24 |
| Frattini | C4 | C23×D37 |
| Fitting | #135×C37 | C2 |
| socle | C2×C37 | C22×D4 |
| hypercenter | #135 | D37 |
| hypocenter | C37 | #578 |
| LCS | G ▷ C4×C37 ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #135 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11924583 | C2 | semidirect |
| 2. #11924566 | C2 | semidirect |
| 3. #11924565 | C2 | semidirect |
| 4. #11924555 | C2 | semidirect |
| 5. C2×Dic148 | C2 | semidirect |
| 6. Q16×D37 | C2 | semidirect |
| 7. #11924542 | C2 | semidirect |
| 8. #135×C37 | C2 | semidirect |
| 60. C37 | #578 | semidirect |
| 65. #135 | D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11924583 | 2 |
| #11924566 | 2 |
| #11924565 | 2 |
| #11924555 | 2 |
| C2×Dic148 | 2 |
| Q16×D37 | 2 |
| #11924542 | 2 |
| #135×C37 | 2 |
| #578 | 37 |