Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
226 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 57 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. C22×Dic764 | C2 | semidirect |
| 2. C2×#20259267 | C2 | semidirect |
| 4. #27132468 | C2 | semidirect |
| 5. C22⋊C16×C191 | C2 | semidirect |
| 26. Dic764 | D4 | semidirect |
| 54. C22×C191 | SD32 | semidirect |
| 69. C191 | #2185 | semidirect |
| 75. C22⋊C16 | D191 | semidirect |
| 127. C22 | #20259267 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic764 | 2 |
| C2×#20259267 | 2 |
| #27132899 | 2 |
| #27132468 | 2 |
| C22⋊C16×C191 | 2 |
| #2185 | 191 |