Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
712 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 115 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×#11763922 | C2 | semidirect |
| 2. C4×C22⋊#3633 | C2 | semidirect |
| 3. C2×D4⋊#3633 | C2 | semidirect |
| 4. #14545792 | C2 | semidirect |
| 53. C4⋊#3633 | D4 | semidirect |
| 57. C17×#121 | C8 | semidirect |
| 59. #10587624 | C8 | semidirect |
| 60. #10587616 | C8 | semidirect |
| 61. #10587581 | C8 | semidirect |
| 289. #121 | #3633 | semidirect |
| 319. C17 | #8940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763922 | 2 |
| C4×C22⋊#3633 | 2 |
| C2×D4⋊#3633 | 2 |
| #14545792 | 2 |
| #121×#595 | 2 |
| #8940 | 17 |