Finite Group DatabasebetaFinite Group DatabasebetaOrder 24896.
162 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 55 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×#20261949 | C2 | semidirect |
| 3. C4⋊C4×D389 | C2 | semidirect |
| 4. #27159308 | C2 | semidirect |
| 5. #27159306 | C2 | semidirect |
| 6. #27159304 | C2 | semidirect |
| 7. #103×C389 | C2 | semidirect |
| 9. #20261967 | C4 | semidirect |
| 26. D1556 | C2×C4 | semidirect |
| 35. Q8×C389 | C2×C4 | semidirect |
| 58. C389 | #417 | semidirect |
| 64. #103 | D389 | semidirect |
| 84. Q8 | C4×D389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20261967 | 2 |
| C2×#20261949 | 2 |
| C4⋊C4×D389 | 2 |
| #27159308 | 2 |
| #27159306 | 2 |
| #27159304 | 2 |
| #103×C389 | 2 |
| #417 | 389 |