Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
290 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 107 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 | #548 |
| 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. C2×#10596962 | C2 | semidirect |
| 2. C22×Dic74 | C2 | semidirect |
| 3. #11924524 | C2 | semidirect |
| 4. #11924522 | C2 | semidirect |
| 5. #11924515 | C2 | semidirect |
| 6. #11924514 | C2 | semidirect |
| 7. #11924510 | C2 | semidirect |
| 8. #11924508 | C2 | semidirect |
| 9. C4×Dic74 | C2 | semidirect |
| 10. #11924496 | C2 | semidirect |
| 11. C4×D4×C37 | C2 | semidirect |
| 58. Dic74 | D4 | semidirect |
| 64. C22×C37 | #41 | semidirect |
| 84. C37 | #548 | semidirect |
| 95. C4×D4 | D37 | semidirect |
| 151. C22 | #10596962 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10596962 | 2 |
| C22×Dic74 | 2 |
| #11924524 | 2 |
| #11924522 | 2 |
| #11924515 | 2 |
| #11924514 | 2 |
| #11924510 | 2 |
| #11924508 | 2 |
| C4×Dic74 | 2 |
| #11924496 | 2 |
| C4×D4×C37 | 2 |
| #548 | 37 |