Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#20259254 | C2 | semidirect |
| 3. C2×#20259247 | C2 | semidirect |
| 5. #27132569 | C2 | semidirect |
| 7. C2×C4×C8×C191 | C2 | semidirect |
| 12. C2×#15690276 | C4 | semidirect |
| 79. C2×C4×C191 | SD16 | semidirect |
| 87. C8×C191 | C22⋊C4 | semidirect |
| 112. C191 | #1968 | semidirect |
| 118. C2×C4×C8 | D191 | semidirect |
| 192. C2×C4 | #15690276 | semidirect |
| 200. C8 | (C2×D191)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15690276 | 2 |
| C2×#20259254 | 2 |
| C2×#20259247 | 2 |
| C2×#20259244 | 2 |
| #27132569 | 2 |
| #27132565 | 2 |
| C2×C4×C8×C191 | 2 |
| #1968 | 191 |