Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
332 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 97 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×C22⋊(C199⋊C8) | C2 | semidirect |
| 3. #27163743 | C2 | semidirect |
| 4. #27163741 | C2 | semidirect |
| 5. C2×C22⋊C8×C199 | C2 | semidirect |
| 27. C2×C22⋊D199 | C8 | semidirect |
| 58. C22×D199 | C2×C8 | semidirect |
| 67. C2×Dic199 | C2×C8 | semidirect |
| 122. C199 | #1459 | semidirect |
| 126. C2×C22⋊C8 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D199 | 2 |
| C2×C22⋊(C199⋊C8) | 2 |
| #27163743 | 2 |
| #27163741 | 2 |
| C2×C22⋊C8×C199 | 2 |
| #1459 | 199 |