Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
212 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 41 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. #11716909 | C2 | semidirect |
| 3. C8×#1044 | C2 | semidirect |
| 4. #11716790 | C2 | semidirect |
| 5. #11716784 | C2 | semidirect |
| 25. C52×C8 | D4 | semidirect |
| 26. #6029 | D4 | semidirect |
| 35. #1044 | M16 | semidirect |
| 76. C52 | #436 | semidirect |
| 120. C8 | D52⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D52⋊C2 | 2 |
| #11716909 | 2 |
| C8×#1044 | 2 |
| #11716790 | 2 |
| #11716784 | 2 |
| #436 | 25 |