Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
440 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 209 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 |
|---|---|---|
| 3. #27132712 | C2 | semidirect |
| 4. #27132710 | C2 | semidirect |
| 5. C2×#20259257 | C2 | semidirect |
| 6. #108×D191 | C2 | semidirect |
| 7. #430×C191 | C2 | semidirect |
| 75. C191 | #2916 | semidirect |
| 81. #430 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133429 | 2 |
| C2×#20259330 | 2 |
| #27132712 | 2 |
| #27132710 | 2 |
| C2×#20259257 | 2 |
| #108×D191 | 2 |
| #430×C191 | 2 |
| #2916 | 191 |