Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
164 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×#20263900 | C2 | semidirect |
| 2. #27164259 | C2 | semidirect |
| 4. #27163846 | C2 | semidirect |
| 5. #27163823 | C2 | semidirect |
| 6. #27163820 | C2 | semidirect |
| 7. C22×C16×C199 | C2 | semidirect |
| 39. C16×C199 | D4 | semidirect |
| 59. C22×C199 | SD32 | semidirect |
| 75. C199 | #2217 | semidirect |
| 78. C22×C16 | D199 | semidirect |
| 115. C16 | C22⋊D199 | semidirect |
| 138. C22 | #20263900 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263900 | 2 |
| #27164259 | 2 |
| #27164254 | 2 |
| #27163846 | 2 |
| #27163823 | 2 |
| #27163820 | 2 |
| C22×C16×C199 | 2 |
| #2217 | 199 |