Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
394 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 90 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. #14545132 | C2 | semidirect |
| 3. C2×#11763734 | C2 | semidirect |
| 5. #14543856 | C2 | semidirect |
| 6. #14543852 | C2 | semidirect |
| 25. #11762594 | C4 | semidirect |
| 26. #11762593 | C4 | semidirect |
| 27. #11762592 | C4 | semidirect |
| 28. C17×#350 | C4 | semidirect |
| 62. C17×M32 | C2×C4 | semidirect |
| 63. C2×C16×C17 | C2×C4 | semidirect |
| 64. #10587483 | C2×C4 | semidirect |
| 65. C2×#63214 | C2×C4 | semidirect |
| 200. #350 | #595 | semidirect |
| 232. M32 | C2×#595 | semidirect |
| 235. C2×C16 | C2×#595 | semidirect |
| 249. C17 | #12934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545438 | 2 |
| #14545132 | 2 |
| C2×#11763734 | 2 |
| #14544670 | 2 |
| #14543856 | 2 |
| #14543852 | 2 |
| #14530410 | 2 |
| #12934 | 17 |