Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
274 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 67 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. #27164066 | C2 | semidirect |
| 2. #27164035 | C2 | semidirect |
| 3. #27164023 | C2 | semidirect |
| 4. #27164002 | C2 | semidirect |
| 5. C2×#20263872 | C2 | semidirect |
| 6. #27163790 | C2 | semidirect |
| 110. C199 | #2048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164066 | 2 |
| #27164035 | 2 |
| #27164023 | 2 |
| #27164002 | 2 |
| C2×#20263872 | 2 |
| #27163790 | 2 |
| C2×AGL(1,ℤ/8)×C199 | 2 |
| #2048 | 199 |