Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 3. #27133007 | C2 | semidirect |
| 4. #27133006 | C2 | semidirect |
| 5. #27133000 | C2 | semidirect |
| 6. #27132995 | C2 | semidirect |
| 7. #27132706 | C2 | semidirect |
| 8. #27132671 | C2 | semidirect |
| 9. C2×#20259247 | C2 | semidirect |
| 11. #427×C191 | C2 | semidirect |
| 126. C191 | #3097 | semidirect |
| 135. #427 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133239 | 2 |
| #27133143 | 2 |
| #27133007 | 2 |
| #27133006 | 2 |
| #27133000 | 2 |
| #27132995 | 2 |
| #27132706 | 2 |
| #27132671 | 2 |
| C2×#20259247 | 2 |
| #27132629 | 2 |
| #427×C191 | 2 |
| #3097 | 191 |