Finite Group DatabasebetaFinite Group DatabasebetaOrder 19648.
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×D307 |
| commutator, socle, cosocle | C22×C307 | C24 |
| Fitting | C22⋊Q8×C307 | C2 |
| hypercenter | C22⋊Q8 | D307 |
| hypocenter | C307 | #562 |
| LCS | G ▷ C22×C307 ▷ C307 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23754250 | C2 | semidirect |
| 2. #23754249 | C2 | semidirect |
| 3. #23754246 | C2 | semidirect |
| 4. #23754245 | C2 | semidirect |
| 5. #23754245 | C2 | semidirect |
| 6. #23754243 | C2 | semidirect |
| 7. #23754242 | C2 | semidirect |
| 8. #23754240 | C2 | semidirect |
| 9. #23754238 | C2 | semidirect |
| 10. #23754236 | C2 | semidirect |
| 11. #23754235 | C2 | semidirect |
| 12. #23754234 | C2 | semidirect |
| 13. #23754233 | C2 | semidirect |
| 14. #23754233 | C2 | semidirect |
| 15. C22⋊Q8×C307 | C2 | semidirect |
| 109. C307 | #562 | semidirect |
| 121. C22⋊Q8 | D307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23754250 | 2 |
| #23754249 | 2 |
| #23754246 | 2 |
| #23754245 | 2 |
| #23754243 | 2 |
| #23754242 | 2 |
| #23754240 | 2 |
| #23754238 | 2 |
| #23754236 | 2 |
| #23754235 | 2 |
| #23754234 | 2 |
| #23754233 | 2 |
| C22⋊Q8×C307 | 2 |
| #562 | 307 |