Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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. #27132719 | C2 | semidirect |
| 3. C4⋊C8×D191 | C2 | semidirect |
| 4. #27132411 | C2 | semidirect |
| 5. #27132411 | C2 | semidirect |
| 6. #27132407 | C2 | semidirect |
| 7. #331×C191 | C2 | semidirect |
| 95. C191 | #1551 | semidirect |
| 103. #331 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133211 | 2 |
| #27132719 | 2 |
| C4⋊C8×D191 | 2 |
| #27132411 | 2 |
| #27132407 | 2 |
| #331×C191 | 2 |
| #1551 | 191 |