Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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×Dic199⋊C8 | C2 | semidirect |
| 5. #27163773 | C2 | semidirect |
| 6. #27163772 | C2 | semidirect |
| 7. C2×C4⋊C8×C199 | C2 | semidirect |
| 43. (C2×D199)⋊C4 | C8 | semidirect |
| 72. C2×Dic199 | C2×C8 | semidirect |
| 85. C2×C4×C199 | C2×C8 | semidirect |
| 107. C2×D199 | C4⋊C8 | semidirect |
| 125. C199 | #1850 | semidirect |
| 129. C2×C4⋊C8 | D199 | semidirect |
| 209. C2×C4 | C8×D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D199 | 2 |
| C2×Dic199⋊C8 | 2 |
| C2×(C2×D199)⋊C8 | 2 |
| C4×(C2×D199)⋊C4 | 2 |
| #27163773 | 2 |
| #27163772 | 2 |
| C2×C4⋊C8×C199 | 2 |
| #1850 | 199 |