Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#20259353 | C2 | semidirect |
| 3. C22×#15690277 | C2 | semidirect |
| 4. #27132823 | C2 | semidirect |
| 5. #27132818 | C2 | semidirect |
| 6. #27132671 | C2 | semidirect |
| 7. #27132657 | C2 | semidirect |
| 8. #27132630 | C2 | semidirect |
| 9. #536×C191 | C2 | semidirect |
| 140. C191 | #3011 | semidirect |
| 145. #536 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259369 | 2 |
| C2×#20259353 | 2 |
| C22×#15690277 | 2 |
| #27132823 | 2 |
| #27132818 | 2 |
| #27132671 | 2 |
| #27132657 | 2 |
| #27132630 | 2 |
| #536×C191 | 2 |
| #3011 | 191 |