Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
546 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 546 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. #41×#3633 | C2 | semidirect |
| 2. #14545903 | C2 | semidirect |
| 3. C2×D4⋊#3633 | C2 | semidirect |
| 4. #14545898 | C2 | semidirect |
| 5. #14545796 | C2 | semidirect |
| 6. #14545791 | C2 | semidirect |
| 70. C17×AGL(1,ℤ/8) | C8 | semidirect |
| 71. #10587635 | C8 | semidirect |
| 72. #10587618 | C8 | semidirect |
| 77. #10587594 | C8 | semidirect |
| 106. C2×D4×C17 | C2×C8 | semidirect |
| 120. C2×D68 | C2×C8 | semidirect |
| 146. M16×C17 | C2×C8 | semidirect |
| 151. #63223 | C2×C8 | semidirect |
| 296. AGL(1,ℤ/8) | #3633 | semidirect |
| 342. C17 | #9095 | semidirect |
| 359. C2×D4 | C2×#3633 | semidirect |
| 383. M16 | C2×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#3633 | 2 |
| #14545903 | 2 |
| C2×D4⋊#3633 | 2 |
| #14545898 | 2 |
| #14545796 | 2 |
| #14545791 | 2 |
| AGL(1,ℤ/8)×#595 | 2 |
| #9095 | 17 |