Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
206 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 53 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. #27133103 | C2 | semidirect |
| 2. C2×#20259268 | C2 | semidirect |
| 3. #27132938 | C2 | semidirect |
| 4. #27132479 | C2 | semidirect |
| 5. #27132470 | C2 | semidirect |
| 6. #27132447 | C2 | semidirect |
| 88. C191 | #2195 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133103 | 2 |
| C2×#20259268 | 2 |
| #27132938 | 2 |
| #27132479 | 2 |
| #27132470 | 2 |
| #27132447 | 2 |
| #578×C191 | 2 |
| #2195 | 191 |