Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
362 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 79 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. #27164492 | C2 | semidirect |
| 3. #27164035 | C2 | semidirect |
| 4. C2×#20263871 | C2 | semidirect |
| 5. #27163775 | C2 | semidirect |
| 6. #27163774 | C2 | semidirect |
| 7. #421×C199 | C2 | semidirect |
| 10. #20263951 | C4 | semidirect |
| 11. #20263944 | C4 | semidirect |
| 43. C4×Dic199 | C2×C4 | semidirect |
| 44. C4×Dic199 | D4 | semidirect |
| 49. C2×Q8×C199 | C2×C4 | semidirect |
| 51. C2×D4×C199 | C2×C4 | semidirect |
| 59. C42×C199 | D4 | semidirect |
| 116. C199 | #1911 | semidirect |
| 121. #421 | D199 | semidirect |
| 147. C2×Q8 | C4×D199 | semidirect |
| 156. C2×D4 | C4×D199 | semidirect |
| 176. C42 | C22⋊D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164582 | 2 |
| #27164492 | 2 |
| #27164035 | 2 |
| C2×#20263871 | 2 |
| #27163775 | 2 |
| #27163774 | 2 |
| #421×C199 | 2 |
| #1911 | 199 |