Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
872 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 237 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×C4×Dic382 | C2 | semidirect |
| 3. #27132565 | C2 | semidirect |
| 4. #27132563 | C2 | semidirect |
| 5. #27132523 | C2 | semidirect |
| 6. #27132522 | C2 | semidirect |
| 7. #27132510 | C2 | semidirect |
| 8. C4×C22⋊C4×C191 | C2 | semidirect |
| 10. C2×#15690287 | C4 | semidirect |
| 60. Dic382 | C22⋊C4 | semidirect |
| 85. C2×C4×C191 | #41 | semidirect |
| 114. C191 | #2341 | semidirect |
| 123. C4×C22⋊C4 | D191 | semidirect |
| 200. C2×C4 | #15690287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15690287 | 2 |
| C2×C4×Dic382 | 2 |
| #27132565 | 2 |
| #27132563 | 2 |
| #27132523 | 2 |
| #27132522 | 2 |
| #27132510 | 2 |
| C4×C22⋊C4×C191 | 2 |
| #2341 | 191 |