Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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. #27164454 | C2 | semidirect |
| 2. #27164136 | C2 | semidirect |
| 3. #27163839 | C2 | semidirect |
| 4. #27163831 | C2 | semidirect |
| 5. #493×C199 | C2 | semidirect |
| 18. Dic796 | D4 | semidirect |
| 20. D1592 | D4 | semidirect |
| 61. C199 | #2213 | semidirect |
| 64. #493 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164454 | 2 |
| #27164136 | 2 |
| #27163839 | 2 |
| #27163831 | 2 |
| #493×C199 | 2 |
| #2213 | 199 |