Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
174 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 49 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×#20259263 | C2 | semidirect |
| 2. C2×C16×D191 | C2 | semidirect |
| 3. #27132900 | C2 | semidirect |
| 4. #27132896 | C2 | semidirect |
| 5. #27132488 | C2 | semidirect |
| 6. #27132465 | C2 | semidirect |
| 7. #357×C191 | C2 | semidirect |
| 33. C191⋊C16 | D4 | semidirect |
| 67. C2×D191 | D16 | semidirect |
| 79. C191 | #2215 | semidirect |
| 87. #357 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259263 | 2 |
| C2×C16×D191 | 2 |
| #27132900 | 2 |
| #27132896 | 2 |
| #27132488 | 2 |
| #27132465 | 2 |
| #357×C191 | 2 |
| #2215 | 191 |