Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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×#20263980 | C2 | semidirect |
| 2. #27164582 | C2 | semidirect |
| 3. #27164035 | C2 | semidirect |
| 4. #27164024 | C2 | semidirect |
| 5. #27163992 | C2 | semidirect |
| 6. #27163789 | C2 | semidirect |
| 7. #575×C199 | C2 | semidirect |
| 42. #15691870 | D4 | semidirect |
| 60. C2×Q8×C199 | D4 | semidirect |
| 64. C2×D4×C199 | D4 | semidirect |
| 74. C2×C8×C199 | D4 | semidirect |
| 142. C199 | #2008 | semidirect |
| 144. #575 | D199 | semidirect |
| 184. C2×Q8 | C22⋊D199 | semidirect |
| 195. C2×D4 | C22⋊D199 | semidirect |
| 210. C2×C8 | C22⋊D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263980 | 2 |
| #27164582 | 2 |
| #27164035 | 2 |
| #27164024 | 2 |
| #27163992 | 2 |
| #27163789 | 2 |
| #575×C199 | 2 |
| #2008 | 199 |