Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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. #27133146 | C2 | semidirect |
| 2. #27133001 | C2 | semidirect |
| 3. #27132996 | C2 | semidirect |
| 4. #27132984 | C2 | semidirect |
| 5. #27132974 | C2 | semidirect |
| 6. #27132703 | C2 | semidirect |
| 7. C2×#20259255 | C2 | semidirect |
| 8. #27132664 | C2 | semidirect |
| 9. #27132659 | C2 | semidirect |
| 10. #27132630 | C2 | semidirect |
| 133. C191 | #3098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133146 | 2 |
| #27133001 | 2 |
| #27132996 | 2 |
| #27132984 | 2 |
| #27132974 | 2 |
| #27132703 | 2 |
| C2×#20259255 | 2 |
| #27132664 | 2 |
| #27132659 | 2 |
| #27132630 | 2 |
| #537×C191 | 2 |
| #3098 | 191 |