Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
370 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 89 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. #27164501 | C2 | semidirect |
| 3. #27164024 | C2 | semidirect |
| 4. #27163920 | C2 | semidirect |
| 5. #27163786 | C2 | semidirect |
| 6. #27163778 | C2 | semidirect |
| 7. C2×#104×C199 | C2 | semidirect |
| 10. #20263980 | C4 | semidirect |
| 34. C2×D796 | C2×C4 | semidirect |
| 40. #15691870 | C2×C4 | semidirect |
| 85. Q8×C199 | C22⋊C4 | semidirect |
| 89. D4×C199 | C22⋊C4 | semidirect |
| 132. C199 | #1883 | semidirect |
| 136. C2×#104 | D199 | semidirect |
| 208. Q8 | (C2×D199)⋊C4 | semidirect |
| 216. D4 | (C2×D199)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263980 | 2 |
| #27164501 | 2 |
| #27164024 | 2 |
| #27163920 | 2 |
| #27163786 | 2 |
| #27163778 | 2 |
| C2×#104×C199 | 2 |
| #1883 | 199 |