Finite Group DatabasebetaFinite Group DatabasebetaOrder 18112.
236 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 95 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 | #124×C283 | C2 |
| hypercenter | #124 | D283 |
| hypocenter | C283 | #555 |
| LCS | G ▷ C22×C283 ▷ C283 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22583608 | C2 | semidirect |
| 2. #22583599 | C2 | semidirect |
| 3. #22583596 | C2 | semidirect |
| 4. #22583583 | C2 | semidirect |
| 5. #22583582 | C2 | semidirect |
| 6. (C22⋊D283)⋊C4 | C2 | semidirect |
| 7. #22583567 | C2 | semidirect |
| 8. #22583566 | C2 | semidirect |
| 9. #124×C283 | C2 | semidirect |
| 66. C283 | #555 | semidirect |
| 71. #124 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22583608 | 2 |
| #22583599 | 2 |
| #22583596 | 2 |
| #22583583 | 2 |
| #22583582 | 2 |
| (C22⋊D283)⋊C4 | 2 |
| #22583567 | 2 |
| #22583566 | 2 |
| #124×C283 | 2 |
| #555 | 283 |