Finite Group DatabasebetaFinite Group DatabasebetaOrder 18112.
236 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 97 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×D283 |
| commutator, socle, cosocle | C22×C283 | C24 |
| Fitting | #117×C283 | C2 |
| hypercenter | #117 | D283 |
| hypocenter | C283 | #555 |
| LCS | G ▷ C22×C283 ▷ C283 | |
| UCS | C1 ◁ C22 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22583609 | C2 | semidirect |
| 2. #22583598 | C2 | semidirect |
| 3. #22583596 | C2 | semidirect |
| 4. #22583585 | C2 | semidirect |
| 5. #22583584 | C2 | semidirect |
| 6. #22583583 | C2 | semidirect |
| 7. #22583572 | C2 | semidirect |
| 8. C4×C22⋊D283 | C2 | semidirect |
| 9. #22583568 | C2 | semidirect |
| 10. #22583567 | C2 | semidirect |
| 11. #117×C283 | C2 | semidirect |
| 78. C283 | #555 | semidirect |
| 90. #117 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22583609 | 2 |
| #22583598 | 2 |
| #22583596 | 2 |
| #22583585 | 2 |
| #22583584 | 2 |
| #22583583 | 2 |
| #22583572 | 2 |
| C4×C22⋊D283 | 2 |
| #22583568 | 2 |
| #22583567 | 2 |
| #117×C283 | 2 |
| #555 | 283 |