Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
224 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 93 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. C22×C191⋊C16 | C2 | semidirect |
| 3. #27132448 | C2 | direct (N × H) |
| 4. C2×M32×C191 | C2 | semidirect |
| 15. C2×C191⋊C16 | C22 | semidirect |
| 18. M32×C191 | C22 | semidirect |
| 79. C2×C191 | #350 | semidirect |
| 82. C191 | C2×#350 | semidirect |
| 85. C2×M32 | D191 | semidirect |
| 98. M32 | C2×D191 | semidirect |
| 163. C2 | #27132448 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259328 | 2 |
| C22×C191⋊C16 | 2 |
| #27132448 | 2 |
| C2×M32×C191 | 2 |
| C2×#350 | 191 |