Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 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. #27132687 | C2 | semidirect |
| 4. #27132423 | C2 | semidirect |
| 5. C4×C4⋊C4×C191 | C2 | semidirect |
| 8. C4×Dic382 | C4 | semidirect |
| 9. C4×Dic382 | C4 | semidirect |
| 10. C4×D764 | C4 | semidirect |
| 11. C4×D764 | C4 | semidirect |
| 60. Dic382 | C4⋊C4 | semidirect |
| 62. D764 | C4⋊C4 | semidirect |
| 101. C4×C191 | #104 | semidirect |
| 115. C191 | #1806 | semidirect |
| 120. C4×C4⋊C4 | D191 | semidirect |
| 220. C4 | #20259250 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15690287 | 2 |
| #27132687 | 2 |
| C2×#20259250 | 2 |
| #27132423 | 2 |
| C4×C4⋊C4×C191 | 2 |
| #1806 | 191 |