Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
572 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#20259343 | C2 | semidirect |
| 2. #27133214 | C2 | semidirect |
| 3. #27133211 | C2 | semidirect |
| 4. #27133044 | C2 | semidirect |
| 5. #27133042 | C2 | semidirect |
| 6. #27133039 | C2 | semidirect |
| 7. #27133036 | C2 | semidirect |
| 8. C4×C8×D191 | C2 | semidirect |
| 9. #492×C191 | C2 | semidirect |
| 47. C8×D191 | D4 | semidirect |
| 91. C4×C191 | #135 | semidirect |
| 101. C191 | #3147 | semidirect |
| 110. #492 | D191 | semidirect |
| 196. C4 | #20259343 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259343 | 2 |
| #27133214 | 2 |
| #27133211 | 2 |
| #27133044 | 2 |
| #27133042 | 2 |
| #27133039 | 2 |
| #27133036 | 2 |
| C4×C8×D191 | 2 |
| #492×C191 | 2 |
| #3147 | 191 |