Finite Group DatabasebetaFinite Group DatabasebetaOrder 24896.
294 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 151 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. C4×Dic778 | C2 | semidirect |
| 3. C4×D1556 | C2 | semidirect |
| 4. #27159344 | C2 | semidirect |
| 5. #27159342 | C2 | semidirect |
| 6. C2×C4⋊Dic389 | C2 | semidirect |
| 7. C4⋊C4×D389 | C2 | semidirect |
| 8. #117×C389 | C2 | semidirect |
| 9. #20261966 | C4 | semidirect |
| 27. Dic778 | C2×C4 | semidirect |
| 28. D1556 | C2×C4 | semidirect |
| 29. C22⋊D389 | C2×C4 | semidirect |
| 34. C4×D389 | C2×C4 | semidirect |
| 36. C2×C4×C389 | C2×C4 | semidirect |
| 59. C389 | #520 | semidirect |
| 66. #117 | D389 | semidirect |
| 96. C2×C4 | C4×D389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20261966 | 2 |
| C4×Dic778 | 2 |
| C4×D1556 | 2 |
| #27159344 | 2 |
| #27159342 | 2 |
| C2×C4⋊Dic389 | 2 |
| C4⋊C4×D389 | 2 |
| #117×C389 | 2 |
| #520 | 389 |