Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
400 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 92 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. #14545136 | C2 | semidirect |
| 3. C2×#11763736 | C2 | semidirect |
| 5. #14543859 | C2 | semidirect |
| 6. #14543846 | 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 |
| 203. #350 | #595 | semidirect |
| 234. M32 | C2×#595 | semidirect |
| 239. C2×C16 | C2×#595 | semidirect |
| 253. C17 | #12926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545439 | 2 |
| #14545136 | 2 |
| C2×#11763736 | 2 |
| #14544673 | 2 |
| #14543859 | 2 |
| #14543846 | 2 |
| D17×#350 | 2 |
| #12926 | 17 |