Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 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. #27133291 | C2 | semidirect |
| 3. #27132973 | C2 | semidirect |
| 4. #27132962 | C2 | semidirect |
| 5. #27132957 | C2 | semidirect |
| 6. #27132942 | C2 | semidirect |
| 7. C2×#20259255 | C2 | semidirect |
| 8. #27132691 | C2 | semidirect |
| 11. #428×C191 | C2 | semidirect |
| 42. #15690287 | Q8 | semidirect |
| 123. C191 | #3083 | semidirect |
| 131. #428 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133291 | 2 |
| #27133144 | 2 |
| #27132973 | 2 |
| #27132962 | 2 |
| #27132957 | 2 |
| #27132942 | 2 |
| C2×#20259255 | 2 |
| #27132691 | 2 |
| #27132665 | 2 |
| #27132657 | 2 |
| #428×C191 | 2 |
| #3083 | 191 |