Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1806 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1806 conjugacy classes of subgroups — too many to draw. Only its 349 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 |
|---|---|---|
| 2. C2×#11763895 | C2 | direct (N × H) |
| 7. #11763895 | C22 | direct (N × H) |
| 27. C23×C4×C17 | C8 | semidirect |
| 28. C23×Dic17 | C8 | semidirect |
| 33. C22×C4×D17 | C8 | semidirect |
| 72. C22×C4×C17 | C2×C8 | semidirect |
| 75. C22×Dic17 | C2×C8 | semidirect |
| 83. C2×C4×D17 | C2×C8 | semidirect |
| 125. C2×C4×C17 | C22×C8 | semidirect |
| 128. C2×Dic17 | C22×C8 | semidirect |
| 138. C22×C17 | #324 | semidirect |
| 151. C2×D17 | #324 | semidirect |
| 176. C2×C17 | C2×#324 | semidirect |
| 180. D17 | C2×#324 | semidirect |
| 200. C23×C4 | #3633 | semidirect |
| 211. C17 | C22×#324 | semidirect |
| 251. C22×C4 | C2×#3633 | semidirect |
| 299. C2×C4 | C22×#3633 | semidirect |
| 319. C22 | #11763895 | direct (N × H) |
| 335. C2 | C2×#11763895 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#3633 | 2 |
| C2×#11763895 | 2 |
| C23×C4⋊#595 | 2 |
| C22×#324 | 17 |