Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
302 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 93 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. #27164061 | C2 | semidirect |
| 4. #27163887 | C2 | semidirect |
| 5. #27163787 | C2 | semidirect |
| 6. #27163777 | C2 | semidirect |
| 15. #20263882 | C4 | semidirect |
| 31. #15691870 | C2×C4 | semidirect |
| 38. C4×Dic199 | C2×C4 | semidirect |
| 69. Q8×C199 | C4⋊C4 | semidirect |
| 73. D4×C199 | C4⋊C4 | semidirect |
| 112. C199 | #1859 | semidirect |
| 175. Q8 | Dic199⋊C4 | semidirect |
| 179. D4 | Dic199⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164061 | 2 |
| C2×#20263882 | 2 |
| #27164019 | 2 |
| #27163887 | 2 |
| #27163787 | 2 |
| #27163777 | 2 |
| #520×C199 | 2 |
| #1859 | 199 |