Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
944 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D283 |
| commutator, socle, cosocle | C23×C283 | C24 |
| Fitting | #395×C283 | C2 |
| hypercenter | #395 | D283 |
| hypocenter | C283 | #2388 |
| LCS | G ▷ C23×C283 ▷ C283 | |
| UCS | C1 ◁ C23 ◁ #395 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#17985393 | C2 | semidirect |
| 2. C2×#22583572 | C2 | semidirect |
| 3. #31826382 | C2 | semidirect |
| 4. #31826376 | C2 | semidirect |
| 5. #31826375 | C2 | semidirect |
| 6. #31826312 | C2 | semidirect |
| 7. #395×C283 | C2 | semidirect |
| 34. C2×C4×D283 | D4 | semidirect |
| 51. C22×D283 | #41 | semidirect |
| 66. C2×C4×C283 | #41 | semidirect |
| 88. C283 | #2388 | semidirect |
| 92. #395 | D283 | semidirect |
| 155. C2×C4 | #17985393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#17985393 | 2 |
| C2×#22583572 | 2 |
| #31826382 | 2 |
| #31826376 | 2 |
| #31826375 | 2 |
| #31826312 | 2 |
| #395×C283 | 2 |
| #2388 | 283 |