Finite Group DatabasebetaFinite Group DatabasebetaOrder 18112.
220 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 91 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 | C22⋊Q8×C283 | C2 |
| hypercenter | C22⋊Q8 | D283 |
| hypocenter | C283 | #562 |
| LCS | G ▷ C22×C283 ▷ C283 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22583600 | C2 | semidirect |
| 2. #22583599 | C2 | semidirect |
| 3. #22583596 | C2 | semidirect |
| 4. #22583595 | C2 | semidirect |
| 5. #22583595 | C2 | semidirect |
| 6. #22583593 | C2 | semidirect |
| 7. #22583592 | C2 | semidirect |
| 8. #22583590 | C2 | semidirect |
| 9. #22583588 | C2 | semidirect |
| 10. #22583586 | C2 | semidirect |
| 11. #22583585 | C2 | semidirect |
| 12. #22583584 | C2 | semidirect |
| 13. #22583583 | C2 | semidirect |
| 14. #22583583 | C2 | semidirect |
| 15. C22⋊Q8×C283 | C2 | semidirect |
| 109. C283 | #562 | semidirect |
| 121. C22⋊Q8 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22583600 | 2 |
| #22583599 | 2 |
| #22583596 | 2 |
| #22583595 | 2 |
| #22583593 | 2 |
| #22583592 | 2 |
| #22583590 | 2 |
| #22583588 | 2 |
| #22583586 | 2 |
| #22583585 | 2 |
| #22583584 | 2 |
| #22583583 | 2 |
| C22⋊Q8×C283 | 2 |
| #562 | 283 |