Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
176 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 71 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. #27164096 | C2 | semidirect |
| 2. #27163769 | C2 | semidirect |
| 3. D4⋊(C199⋊C8) | C2 | semidirect |
| 4. #27163739 | C2 | semidirect |
| 41. C8×C199 | M16 | semidirect |
| 55. C199 | #1594 | semidirect |
| 97. C8 | #15691870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164096 | 2 |
| #27163769 | 2 |
| D4⋊(C199⋊C8) | 2 |
| #27163739 | 2 |
| C4×D8×C199 | 2 |
| #1594 | 199 |