Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1010 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1010 conjugacy classes of subgroups — too many to draw. Only its 251 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 |
|---|---|---|
| 3. #14527924 | C2 | direct (N × H) |
| 71. C2×Q8×C17 | Q16 | semidirect |
| 110. Q8×C17 | C2×Q16 | semidirect |
| 168. C2×C17 | #1633 | semidirect |
| 209. C17 | C2×#1633 | semidirect |
| 219. C2×Q8 | #63231 | semidirect |
| 256. Q8 | C2×#63231 | semidirect |
| 286. C2 | #14527924 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763188 | 2 |
| C2×#11763104 | 2 |
| #14527924 | 2 |
| C2×#11762558 | 2 |
| C2×Q8⋊#3622 | 2 |
| C2×Q82×C17 | 2 |
| C2×#1633 | 17 |