Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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×#20259287 | C2 | semidirect |
| 3. #27132998 | C2 | semidirect |
| 4. #27132973 | C2 | semidirect |
| 5. #27132884 | C2 | semidirect |
| 6. #27132821 | C2 | semidirect |
| 8. #27132769 | C2 | semidirect |
| 9. #27132760 | C2 | semidirect |
| 10. #27132717 | C2 | semidirect |
| 131. C191 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133194 | 2 |
| C2×#20259287 | 2 |
| #27132998 | 2 |
| #27132973 | 2 |
| #27132884 | 2 |
| #27132821 | 2 |
| #27132801 | 2 |
| #27132769 | 2 |
| #27132760 | 2 |
| #27132717 | 2 |
| #481×C191 | 2 |
| #3117 | 191 |