Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
186 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 59 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×#87739 | C2 | semidirect |
| 2. C22×#6016 | C2 | semidirect |
| 4. C22⋊#6016 | C2 | semidirect |
| 5. C22⋊#6016 | C2 | semidirect |
| 6. #11716419 | C2 | semidirect |
| 7. #11716417 | C2 | semidirect |
| 37. #6016 | D4 | semidirect |
| 50. C22×C25 | M16 | semidirect |
| 100. C25 | #435 | semidirect |
| 154. C22 | #87739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87739 | 2 |
| C22×#6016 | 2 |
| D4×Dic25 | 2 |
| C22⋊#6016 | 2 |
| #11716419 | 2 |
| #11716417 | 2 |
| #65773 | 5 |