Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
316 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 81 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. #27164075 | C2 | semidirect |
| 3. #27163747 | C2 | semidirect |
| 4. C4×M16×C199 | C2 | semidirect |
| 13. C4⋊(C199⋊C8) | C22 | semidirect |
| 19. C4×C8×C199 | C22 | semidirect |
| 48. D796 | M16 | semidirect |
| 85. C199 | #1490 | semidirect |
| 89. C4×M16 | D199 | semidirect |
| 105. C4×C8 | C2×D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D796 | 2 |
| #27164075 | 2 |
| #27163747 | 2 |
| C4×M16×C199 | 2 |
| #1490 | 199 |