Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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. #27164074 | C2 | semidirect |
| 3. #27164069 | C2 | semidirect |
| 4. #27163747 | C2 | semidirect |
| 5. D4⋊(C199⋊C8) | C2 | semidirect |
| 6. #27163745 | C2 | semidirect |
| 7. D4⋊C8×C199 | C2 | semidirect |
| 115. C199 | #1496 | semidirect |
| 123. D4⋊C8 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164565 | 2 |
| #27164074 | 2 |
| #27164069 | 2 |
| #27163747 | 2 |
| D4⋊(C199⋊C8) | 2 |
| #27163745 | 2 |
| D4⋊C8×C199 | 2 |
| #1496 | 199 |