Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
428 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 141 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×#20259322 | C2 | semidirect |
| 3. #27133036 | C2 | semidirect |
| 4. #27133014 | C2 | semidirect |
| 5. #27132869 | C2 | semidirect |
| 6. #27132804 | C2 | semidirect |
| 7. #431×C191 | C2 | semidirect |
| 72. C2×C4×C191 | SD16 | semidirect |
| 100. C191 | #3206 | semidirect |
| 108. #431 | D191 | semidirect |
| 173. C2×C4 | #15690276 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133213 | 2 |
| C2×#20259322 | 2 |
| #27133036 | 2 |
| #27133014 | 2 |
| #27132869 | 2 |
| #27132804 | 2 |
| #431×C191 | 2 |
| #3206 | 191 |