Finite Group DatabasebetaFinite Group DatabasebetaOrder 24896.
124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 1. C2×#20261953 | C2 | semidirect |
| 2. C22×#15691005 | C2 | semidirect |
| 4. #27159315 | C2 | semidirect |
| 5. #27159308 | C2 | semidirect |
| 6. #27159304 | C2 | semidirect |
| 7. C22⋊Q8×C389 | C2 | semidirect |
| 27. #15691005 | D4 | semidirect |
| 39. C22×C389 | SD16 | semidirect |
| 55. C389 | #465 | semidirect |
| 59. C22⋊Q8 | D389 | semidirect |
| 98. C22 | #20261953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20261953 | 2 |
| C22×#15691005 | 2 |
| #27159358 | 2 |
| #27159315 | 2 |
| #27159308 | 2 |
| #27159304 | 2 |
| C22⋊Q8×C389 | 2 |
| #465 | 389 |