Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
582 conjugacy classes of subgroups; only the 333 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 333 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. Q8×#63241 | C2 | direct (N × H) |
| 18. C2×#63241 | Q8 | direct (N × H) |
| 28. C2×Q8×C17 | C16 | semidirect |
| 40. #63241 | C2×Q8 | direct (N × H) |
| 46. Q8×C17 | C2×C16 | semidirect |
| 81. C2×C17 | Q8×C16 | semidirect |
| 99. C17 | C2×Q8×C16 | semidirect |
| 100. C2×Q8 | #63241 | direct (N × H) |
| 117. Q8 | C2×#63241 | direct (N × H) |
| 139. C2 | Q8×#63241 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#63241 | 2 |
| C2×C4⋊#63241 | 2 |
| C2×C4×#63241 | 2 |
| C2×Q8×#3624 | 2 |
| C2×Q8×C16 | 17 |