Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
180 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 73 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. #27163771 | C2 | semidirect |
| 3. D4⋊(C199⋊C8) | C2 | semidirect |
| 4. C8×C199⋊C8 | C2 | semidirect |
| 32. C199⋊C8 | D8 | semidirect |
| 43. C8×C199 | M16 | semidirect |
| 58. C199 | #1589 | semidirect |
| 102. C8 | #15691870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164096 | 2 |
| #27163771 | 2 |
| D4⋊(C199⋊C8) | 2 |
| C8×C199⋊C8 | 2 |
| C4×D8×C199 | 2 |
| #1589 | 199 |