Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 3. #27132672 | C2 | semidirect |
| 5. #27132420 | C2 | semidirect |
| 6. #27132419 | C2 | semidirect |
| 7. #419×C191 | C2 | semidirect |
| 13. #20259320 | C4 | semidirect |
| 14. #20259311 | C4 | semidirect |
| 109. C191 | #1909 | semidirect |
| 114. #419 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133429 | 2 |
| #27133237 | 2 |
| #27132672 | 2 |
| #27132636 | 2 |
| #27132420 | 2 |
| #27132419 | 2 |
| #419×C191 | 2 |
| #1909 | 191 |