Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 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. #27132556 | C2 | semidirect |
| 3. #27132556 | C2 | semidirect |
| 4. #27132549 | C2 | semidirect |
| 6. C4⋊C4×Dic191 | C2 | semidirect |
| 7. C22⋊C4×Dic191 | C2 | semidirect |
| 8. C4×C22⋊Dic191 | C2 | semidirect |
| 28. #123×C191 | C4 | semidirect |
| 55. C22×C4×C191 | C2×C4 | semidirect |
| 59. C4⋊C4×C191 | C2×C4 | semidirect |
| 61. C22⋊C4×C191 | C2×C4 | semidirect |
| 126. C191 | #2374 | semidirect |
| 140. #123 | Dic191 | semidirect |
| 172. C22×C4 | C2×Dic191 | semidirect |
| 178. C4⋊C4 | C2×Dic191 | semidirect |
| 184. C22⋊C4 | C2×Dic191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27132566 | 2 |
| #27132556 | 2 |
| #27132549 | 2 |
| #27132543 | 2 |
| C4⋊C4×Dic191 | 2 |
| C22⋊C4×Dic191 | 2 |
| C4×C22⋊Dic191 | 2 |
| C2×#123×C191 | 2 |
| #2374 | 191 |