Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
516 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 516 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 |
|---|---|---|
| 1. #14545437 | C2 | semidirect |
| 2. #14545106 | C2 | semidirect |
| 3. #14545018 | C2 | semidirect |
| 4. #14543851 | C2 | semidirect |
| 17. #11763064 | C4 | semidirect |
| 18. #11763063 | C4 | semidirect |
| 19. #11763062 | C4 | semidirect |
| 24. C17×#470 | C4 | semidirect |
| 34. C2×Q16×C17 | C2×C4 | semidirect |
| 45. C2×D136 | C2×C4 | semidirect |
| 60. #10587533 | D4 | semidirect |
| 63. C17×#106 | C2×C4 | semidirect |
| 67. #10587488 | C2×C4 | semidirect |
| 203. #470 | #595 | semidirect |
| 227. C2×Q16 | C2×#595 | semidirect |
| 263. #106 | C2×#595 | semidirect |
| 268. C17 | #13008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545437 | 2 |
| #14545106 | 2 |
| #14545018 | 2 |
| #14543851 | 2 |
| #14538395 | 2 |
| #13008 | 17 |