Finite Group DatabasebetaFinite Group DatabasebetaOrder 19904.
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×D311 |
| commutator, socle, cosocle | C22×C311 | C24 |
| Fitting | C22⋊Q8×C311 | C2 |
| hypercenter | C22⋊Q8 | D311 |
| hypocenter | C311 | #562 |
| LCS | G ▷ C22×C311 ▷ C311 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23755698 | C2 | semidirect |
| 2. #23755697 | C2 | semidirect |
| 3. #23755694 | C2 | semidirect |
| 4. #23755693 | C2 | semidirect |
| 5. #23755693 | C2 | semidirect |
| 6. #23755691 | C2 | semidirect |
| 7. #23755690 | C2 | semidirect |
| 8. #23755688 | C2 | semidirect |
| 9. #23755686 | C2 | semidirect |
| 10. #23755684 | C2 | semidirect |
| 11. #23755683 | C2 | semidirect |
| 12. #23755682 | C2 | semidirect |
| 13. #23755681 | C2 | semidirect |
| 14. #23755681 | C2 | semidirect |
| 15. C22⋊Q8×C311 | C2 | semidirect |
| 109. C311 | #562 | semidirect |
| 121. C22⋊Q8 | D311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23755698 | 2 |
| #23755697 | 2 |
| #23755694 | 2 |
| #23755693 | 2 |
| #23755691 | 2 |
| #23755690 | 2 |
| #23755688 | 2 |
| #23755686 | 2 |
| #23755684 | 2 |
| #23755683 | 2 |
| #23755682 | 2 |
| #23755681 | 2 |
| C22⋊Q8×C311 | 2 |
| #562 | 311 |