Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 2. C2×Q8×Dic191 | C2 | semidirect |
| 5. #27132552 | C2 | semidirect |
| 6. #27132537 | C2 | semidirect |
| 7. #27132532 | C2 | semidirect |
| 8. #27132509 | C2 | semidirect |
| 9. #391×C191 | C2 | semidirect |
| 12. #20259311 | C4 | semidirect |
| 45. (C2×D191)⋊C4 | C2×C4 | semidirect |
| 47. C4×Dic191 | C2×C4 | semidirect |
| 51. C2×Q8×C191 | C2×C4 | semidirect |
| 111. C191 | #2326 | semidirect |
| 116. #391 | D191 | semidirect |
| 145. C2×Q8 | C4×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259311 | 2 |
| C2×Q8×Dic191 | 2 |
| C2×#20259284 | 2 |
| #27132565 | 2 |
| #27132552 | 2 |
| #27132537 | 2 |
| #27132532 | 2 |
| #27132509 | 2 |
| #391×C191 | 2 |
| #2326 | 191 |