Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
514 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 97 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×#3633)⋊Q8 | C2 | semidirect |
| 3. #14545905 | C2 | semidirect |
| 5. #14545796 | C2 | semidirect |
| 6. #14545791 | C2 | semidirect |
| 70. C17×#137 | C8 | semidirect |
| 71. #10587637 | C8 | semidirect |
| 72. #10587628 | C8 | semidirect |
| 77. #10587595 | C8 | semidirect |
| 102. C2×Q8×C17 | C2×C8 | semidirect |
| 119. C2×Dic34 | C2×C8 | semidirect |
| 145. M16×C17 | C2×C8 | semidirect |
| 150. #63223 | C2×C8 | semidirect |
| 282. #137 | #3633 | semidirect |
| 329. C17 | #8953 | semidirect |
| 343. C2×Q8 | C2×#3633 | semidirect |
| 366. M16 | C2×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14546028 | 2 |
| (C2×#3633)⋊Q8 | 2 |
| #14545905 | 2 |
| #14545902 | 2 |
| #14545796 | 2 |
| #14545791 | 2 |
| #137×#595 | 2 |
| #8953 | 17 |