Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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. #27133131 | C2 | semidirect |
| 3. #27132679 | C2 | semidirect |
| 4. C2×#20259248 | C2 | semidirect |
| 5. #27132636 | C2 | semidirect |
| 6. #27132424 | C2 | semidirect |
| 7. #344×C191 | C2 | semidirect |
| 11. #20259355 | C4 | semidirect |
| 13. #20259350 | C4 | semidirect |
| 37. C2×Dic382 | C2×C4 | semidirect |
| 39. C2×D764 | C2×C4 | semidirect |
| 64. M16×C191 | C2×C4 | semidirect |
| 129. C191 | #1906 | semidirect |
| 136. #344 | D191 | semidirect |
| 185. M16 | C4×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133463 | 2 |
| #27133131 | 2 |
| #27132679 | 2 |
| C2×#20259248 | 2 |
| #27132636 | 2 |
| #27132424 | 2 |
| #344×C191 | 2 |
| #1906 | 191 |