Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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. #27164571 | C2 | semidirect |
| 5. #27163790 | C2 | semidirect |
| 6. #27163777 | C2 | semidirect |
| 7. H(3,ℤ/4)×C199 | C2 | semidirect |
| 28. C2×Dic398 | Q8 | semidirect |
| 29. C2×D796 | Q8 | semidirect |
| 102. C199 | #2031 | semidirect |
| 110. H(3,ℤ/4) | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164571 | 2 |
| #27164036 | 2 |
| C2×#20263881 | 2 |
| #27163991 | 2 |
| #27163790 | 2 |
| #27163777 | 2 |
| H(3,ℤ/4)×C199 | 2 |
| #2031 | 199 |