Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
612 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 612 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 |
|---|---|---|
| 2. #14544960 | C2 | semidirect |
| 3. #14544176 | C2 | semidirect |
| 5. #14543671 | C2 | semidirect |
| 6. #14543636 | C2 | semidirect |
| 25. #11763090 | C4 | semidirect |
| 26. #11763089 | C4 | semidirect |
| 27. #11763011 | C4 | semidirect |
| 32. C17×#461 | C4 | semidirect |
| 45. C17×C4⋊Q8 | C2×C4 | semidirect |
| 62. #10587555 | C2×C4 | semidirect |
| 73. C17×C4⋊C8 | C2×C4 | semidirect |
| 82. C4⋊#3622 | C2×C4 | semidirect |
| 231. #461 | #595 | semidirect |
| 263. C4⋊Q8 | C2×#595 | semidirect |
| 290. C4⋊C8 | C2×#595 | semidirect |
| 306. C17 | #9323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545223 | 2 |
| #14544960 | 2 |
| #14544176 | 2 |
| #14544124 | 2 |
| #14543671 | 2 |
| #14543636 | 2 |
| #14538882 | 2 |
| #9323 | 17 |