Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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. #27164816 | C2 | semidirect |
| 2. C2×#20263983 | C2 | semidirect |
| 3. #27164582 | C2 | semidirect |
| 4. #27164022 | C2 | semidirect |
| 5. #27163991 | C2 | semidirect |
| 6. #27163790 | C2 | semidirect |
| 7. #421×C199 | C2 | semidirect |
| 36. C2×Dic398 | D4 | semidirect |
| 43. C2×D796 | D4 | semidirect |
| 55. C2×C199⋊C8 | D4 | semidirect |
| 70. M16×C199 | D4 | semidirect |
| 142. C199 | #2008 | semidirect |
| 147. #421 | D199 | semidirect |
| 208. M16 | C22⋊D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164816 | 2 |
| C2×#20263983 | 2 |
| #27164582 | 2 |
| #27164022 | 2 |
| #27163991 | 2 |
| #27163790 | 2 |
| #421×C199 | 2 |
| #2008 | 199 |