Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
466 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 466 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 |
|---|---|---|
| 2. #14545928 | C2 | semidirect |
| 3. #14545909 | C2 | semidirect |
| 5. #14545796 | C2 | semidirect |
| 6. #14545789 | C2 | semidirect |
| 68. C17×#104 | C8 | semidirect |
| 69. #10587508 | C8 | semidirect |
| 70. #10587496 | C8 | semidirect |
| 71. #10587476 | C8 | semidirect |
| 119. M16×C17 | C2×C8 | semidirect |
| 120. C42×C17 | C2×C8 | semidirect |
| 122. C4×Dic17 | C2×C8 | semidirect |
| 123. #63223 | C2×C8 | semidirect |
| 149. Q8×C17 | C4⋊C8 | semidirect |
| 151. D4×C17 | C4⋊C8 | semidirect |
| 162. D68 | C4⋊C8 | semidirect |
| 173. Dic34 | C4⋊C8 | semidirect |
| 271. #104 | #3633 | semidirect |
| 280. C17 | #8839 | semidirect |
| 302. M16 | C2×#3633 | semidirect |
| 334. C42 | C2×#3633 | semidirect |
| 339. Q8 | C4⋊#3633 | semidirect |
| 346. D4 | C4⋊#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14546028 | 2 |
| #14545928 | 2 |
| #14545909 | 2 |
| #14545903 | 2 |
| #14545796 | 2 |
| #14545789 | 2 |
| #104×#595 | 2 |
| #8839 | 17 |