Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
648 conjugacy classes of subgroups; only the 315 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 315 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. #11716702 | C2 | direct (N × H) |
| 7. C2×C52×Q8 | C4 | semidirect |
| 20. C52×Q8 | C2×C4 | semidirect |
| 45. C2×C5×Q8 | Dic5 | semidirect |
| 55. C2×C52 | #103 | semidirect |
| 62. C5×Q8 | C2×Dic5 | semidirect |
| 76. C52 | C2×#103 | semidirect |
| 88. C2×Q8 | #1039 | semidirect |
| 97. C2×C5 | #3967 | semidirect |
| 104. Q8 | C2×#1039 | semidirect |
| 114. C5 | C2×#3967 | semidirect |
| 124. C2 | #11716702 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×Q8 | 2 |
| C2×C4⋊#1039 | 2 |
| C22×#6029 | 2 |
| #11716702 | 2 |
| C2×#3967 | 5 |