Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 173 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. #27132558 | C2 | semidirect |
| 3. #27132557 | C2 | semidirect |
| 4. #27132551 | C2 | semidirect |
| 5. #27132547 | C2 | semidirect |
| 7. #27132535 | C2 | semidirect |
| 8. #27132521 | C2 | semidirect |
| 12. #20259303 | C4 | semidirect |
| 36. C22×Dic191 | C2×C4 | semidirect |
| 44. Dic191⋊C4 | C2×C4 | semidirect |
| 48. C22⋊Dic191 | C2×C4 | semidirect |
| 126. C191 | #2376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259303 | 2 |
| #27132558 | 2 |
| #27132557 | 2 |
| #27132551 | 2 |
| #27132547 | 2 |
| #27132543 | 2 |
| #27132535 | 2 |
| #27132521 | 2 |
| #390×C191 | 2 |
| #2376 | 191 |