Finite Group DatabasebetaFinite Group DatabasebetaOrder 24896.
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 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×#20261950 | C2 | semidirect |
| 3. #27159312 | C2 | direct (N × H) |
| 4. C2×C42×C389 | C2 | semidirect |
| 7. #20261966 | C4 | semidirect |
| 9. C2×Dic778 | C4 | semidirect |
| 10. C2×D1556 | C4 | semidirect |
| 14. #20261950 | C22 | semidirect |
| 19. C42×C389 | C22 | semidirect |
| 22. Dic778 | C2×C4 | semidirect |
| 24. D1556 | C2×C4 | semidirect |
| 54. C2×C389 | #104 | semidirect |
| 57. C389 | C2×#104 | semidirect |
| 61. C2×C42 | D389 | semidirect |
| 77. C42 | C2×D389 | semidirect |
| 113. C2 | #27159312 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20261966 | 2 |
| C2×#20261950 | 2 |
| #27159312 | 2 |
| C2×C42×C389 | 2 |
| C2×#104 | 389 |