Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
244 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
| 4. #27163789 | C2 | semidirect |
| 5. #27163779 | C2 | semidirect |
| 6. #27163774 | C2 | semidirect |
| 44. C2×Q8×C199 | Q8 | semidirect |
| 46. C2×D4×C199 | Q8 | semidirect |
| 102. C199 | #2031 | semidirect |
| 131. C2×Q8 | Dic398 | semidirect |
| 133. C2×D4 | Dic398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164571 | 2 |
| C2×#20263882 | 2 |
| #27163992 | 2 |
| #27163789 | 2 |
| #27163779 | 2 |
| #27163774 | 2 |
| #421×C199 | 2 |
| #2031 | 199 |