Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
316 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#20263888 | C2 | semidirect |
| 3. C2×#20263886 | C2 | semidirect |
| 5. #27163780 | C2 | semidirect |
| 6. #27163780 | C2 | semidirect |
| 18. C22⋊(C199⋊C8) | C4 | semidirect |
| 120. C199 | #1854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263914 | 2 |
| C2×#20263888 | 2 |
| C2×#20263886 | 2 |
| C2×C22⋊(C199⋊C8) | 2 |
| #27163780 | 2 |
| #380×C199 | 2 |
| #1854 | 199 |