Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
650 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 84 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. #14545223 | C2 | semidirect |
| 2. #14544947 | C2 | semidirect |
| 3. #14544175 | C2 | semidirect |
| 4. #14544124 | C2 | semidirect |
| 5. #14543671 | C2 | semidirect |
| 6. #14543636 | C2 | semidirect |
| 25. #11763096 | C4 | semidirect |
| 26. #11763005 | C4 | semidirect |
| 27. #11763004 | C4 | semidirect |
| 32. C17×#476 | C4 | semidirect |
| 45. C17×C4⋊Q8 | C2×C4 | semidirect |
| 60. #10587560 | C2×C4 | semidirect |
| 75. C17×C4⋊C8 | C2×C4 | semidirect |
| 83. C4⋊#3622 | C2×C4 | semidirect |
| 164. D4×C17 | #104 | semidirect |
| 184. D68 | #104 | semidirect |
| 239. #476 | #595 | semidirect |
| 274. C4⋊Q8 | C2×#595 | semidirect |
| 301. C4⋊C8 | C2×#595 | semidirect |
| 318. C17 | #9325 | semidirect |
| 397. D4 | #10587550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545223 | 2 |
| #14544947 | 2 |
| #14544175 | 2 |
| #14544124 | 2 |
| #14543671 | 2 |
| #14543636 | 2 |
| #14538877 | 2 |
| #9325 | 17 |