Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 125 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. #27133143 | C2 | semidirect |
| 3. #27133007 | C2 | semidirect |
| 4. #27133000 | C2 | semidirect |
| 5. #27132989 | C2 | semidirect |
| 6. #27132978 | C2 | semidirect |
| 7. C2×#20259255 | C2 | semidirect |
| 8. #27132665 | C2 | semidirect |
| 9. #27132657 | C2 | semidirect |
| 10. #27132631 | C2 | semidirect |
| 11. #428×C191 | C2 | semidirect |
| 133. C191 | #3098 | semidirect |
| 141. #428 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133244 | 2 |
| #27133143 | 2 |
| #27133007 | 2 |
| #27133000 | 2 |
| #27132989 | 2 |
| #27132978 | 2 |
| C2×#20259255 | 2 |
| #27132665 | 2 |
| #27132657 | 2 |
| #27132631 | 2 |
| #428×C191 | 2 |
| #3098 | 191 |