Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
148 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 47 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. C2×#20263896 | C2 | semidirect |
| 2. #27164435 | C2 | semidirect |
| 3. #27164288 | C2 | semidirect |
| 4. #27163847 | C2 | semidirect |
| 5. #27163831 | C2 | semidirect |
| 6. #27163830 | C2 | semidirect |
| 7. #472×C199 | C2 | semidirect |
| 73. C199 | #2221 | semidirect |
| 78. #472 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263896 | 2 |
| #27164435 | 2 |
| #27164288 | 2 |
| #27163847 | 2 |
| #27163831 | 2 |
| #27163830 | 2 |
| #472×C199 | 2 |
| #2221 | 199 |