Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
520 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 267 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 |
|---|---|---|
| 4. #11716682 | C2 | semidirect |
| 5. C8×#1039 | C2 | semidirect |
| 7. C52×M16 | C4 | semidirect |
| 12. C2×#6029 | C4 | semidirect |
| 38. C5×M16 | Dic5 | semidirect |
| 64. C52 | #405 | semidirect |
| 73. M16 | #1039 | semidirect |
| 93. C5 | #65411 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×M16 | 2 |
| #11717246 | 2 |
| C22×#6029 | 2 |
| #11716682 | 2 |
| C8×#1039 | 2 |
| #65411 | 5 |