Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
566 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 97 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. #14546028 | C2 | semidirect |
| 2. #14545934 | C2 | semidirect |
| 3. #14545904 | C2 | semidirect |
| 4. #14545902 | C2 | semidirect |
| 5. #14545796 | C2 | semidirect |
| 6. #14545791 | C2 | semidirect |
| 71. C17×AGL(1,ℤ/8) | C8 | semidirect |
| 72. #10587635 | C8 | semidirect |
| 73. #10587618 | C8 | semidirect |
| 78. #10587594 | C8 | semidirect |
| 108. C2×D4×C17 | C2×C8 | semidirect |
| 122. C2×D68 | C2×C8 | semidirect |
| 148. M16×C17 | C2×C8 | semidirect |
| 153. #63223 | C2×C8 | semidirect |
| 189. Q8×C17 | C22⋊C8 | semidirect |
| 193. D4×C17 | C22⋊C8 | semidirect |
| 206. D68 | C22⋊C8 | semidirect |
| 215. Dic34 | C22⋊C8 | semidirect |
| 298. AGL(1,ℤ/8) | #3633 | semidirect |
| 345. C17 | #8954 | semidirect |
| 362. C2×D4 | C2×#3633 | semidirect |
| 386. M16 | C2×#3633 | semidirect |
| 426. Q8 | C22⋊#3633 | semidirect |
| 439. D4 | C22⋊#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14546028 | 2 |
| #14545934 | 2 |
| #14545904 | 2 |
| #14545902 | 2 |
| #14545796 | 2 |
| #14545791 | 2 |
| AGL(1,ℤ/8)×#595 | 2 |
| #8954 | 17 |