Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
176 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 63 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. #27164097 | C2 | semidirect |
| 3. #27163768 | C2 | semidirect |
| 4. D4⋊(C199⋊C8) | C2 | semidirect |
| 5. #27163745 | C2 | semidirect |
| 6. #27163740 | C2 | semidirect |
| 7. #436×C199 | C2 | semidirect |
| 51. C199⋊C8 | M16 | semidirect |
| 83. C199 | #1594 | semidirect |
| 87. #436 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15691871 | 2 |
| #27164097 | 2 |
| #27163768 | 2 |
| D4⋊(C199⋊C8) | 2 |
| #27163745 | 2 |
| #27163740 | 2 |
| #436×C199 | 2 |
| #1594 | 199 |