Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
592 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 125 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×#20263880 | C2 | semidirect |
| 3. C2×#20263879 | C2 | semidirect |
| 4. C2×#20263878 | C2 | semidirect |
| 7. C2×#103×C199 | C2 | semidirect |
| 15. C2×Q8×D199 | C4 | semidirect |
| 87. Dic398 | C22⋊C4 | semidirect |
| 107. Q8×C199 | C22⋊C4 | semidirect |
| 134. C2×D199 | #103 | semidirect |
| 152. C199 | #1787 | semidirect |
| 158. C2×#103 | D199 | semidirect |
| 245. Q8 | (C2×D199)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D199 | 2 |
| C2×#20263880 | 2 |
| C2×#20263879 | 2 |
| C2×#20263878 | 2 |
| C2×(C2×D199)⋊C8 | 2 |
| #27163875 | 2 |
| C2×#103×C199 | 2 |
| #1787 | 199 |