Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
206 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
| prime radical | C22×D37 | C23 |
| hypercenter | #125 | D37 |
| hypocenter | C37 | #544 |
| 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. #11924536 | C2 | semidirect |
| 2. #11924535 | C2 | semidirect |
| 3. #11924535 | C2 | semidirect |
| 4. #11924527 | C2 | semidirect |
| 5. #11924526 | C2 | semidirect |
| 11. #125×C37 | C2 | semidirect |
| 47. C4×D37 | Q8 | semidirect |
| 69. C37 | #544 | semidirect |
| 75. #125 | D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11924536 | 2 |
| #11924535 | 2 |
| #11924527 | 2 |
| #11924526 | 2 |
| #11924516 | 2 |
| #11924514 | 2 |
| #11924494 | 2 |
| #11924493 | 2 |
| C4⋊C4×D37 | 2 |
| #125×C37 | 2 |
| #544 | 37 |