Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27133211 | C2 | semidirect |
| 2. C4×#15690286 | C2 | semidirect |
| 3. #27132986 | C2 | semidirect |
| 4. #27132949 | C2 | semidirect |
| 5. #27132943 | C2 | semidirect |
| 6. #27132860 | C2 | semidirect |
| 7. #27132805 | C2 | semidirect |
| 8. #27132775 | C2 | semidirect |
| 9. #27132760 | C2 | semidirect |
| 10. #27132719 | C2 | semidirect |
| 11. #459×C191 | C2 | semidirect |
| 86. Dic382 | #41 | semidirect |
| 110. D4×C191 | #41 | semidirect |
| 144. C191 | #3115 | semidirect |
| 152. #459 | D191 | semidirect |
| 241. D4 | #15690286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133211 | 2 |
| C4×#15690286 | 2 |
| #27132986 | 2 |
| #27132949 | 2 |
| #27132943 | 2 |
| #27132860 | 2 |
| #27132805 | 2 |
| #27132775 | 2 |
| #27132760 | 2 |
| #27132719 | 2 |
| #459×C191 | 2 |
| #3115 | 191 |