Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
522 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 522 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. #14545538 | C2 | semidirect |
| 2. D17⋊#360 | C2 | semidirect |
| 3. #14545093 | C2 | semidirect |
| 4. #14544933 | C2 | semidirect |
| 5. #14543856 | C2 | semidirect |
| 6. #14543830 | C2 | semidirect |
| 24. #11763247 | C4 | semidirect |
| 26. #11763245 | C4 | semidirect |
| 27. #11763244 | C4 | semidirect |
| 32. C17×#509 | C4 | semidirect |
| 46. C2×D8×C17 | C2×C4 | semidirect |
| 60. C2×D136 | C2×C4 | semidirect |
| 76. C17×M32 | C2×C4 | semidirect |
| 81. #10587483 | C2×C4 | semidirect |
| 122. Q16×C17 | C22⋊C4 | semidirect |
| 126. D8×C17 | C22⋊C4 | semidirect |
| 135. Dic68 | C22⋊C4 | semidirect |
| 138. D136 | C22⋊C4 | semidirect |
| 232. #509 | #595 | semidirect |
| 274. C2×D8 | C2×#595 | semidirect |
| 298. M32 | C2×#595 | semidirect |
| 310. C17 | #13025 | semidirect |
| 335. Q16 | C22⋊#595 | semidirect |
| 348. D8 | C22⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545538 | 2 |
| D17⋊#360 | 2 |
| #14545093 | 2 |
| #14544933 | 2 |
| #14543856 | 2 |
| #14543830 | 2 |
| D17×#509 | 2 |
| #13025 | 17 |