Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1910 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 1910 conjugacy classes of subgroups — too many to draw. Only its 297 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. H(5,𝔽2)×Dic17 | C2 | semidirect |
| 2. #120×Dic17 | C2 | semidirect |
| 3. #14529193 | C2 | semidirect |
| 4. #14529067 | C2 | semidirect |
| 5. #14528732 | C2 | semidirect |
| 6. #99×Dic17 | C2 | semidirect |
| 8. C24×Dic17 | C22 | semidirect |
| 20. #11762684 | C22 | semidirect |
| 21. #11762665 | C22 | semidirect |
| 23. C22⋊C4×Dic17 | C22 | semidirect |
| 24. #11762575 | C22 | semidirect |
| 27. C17×B(4,𝔽2) | C4 | semidirect |
| 31. C17×H(5,𝔽2) | C2×C4 | semidirect |
| 40. C23×Dic17 | D4 | semidirect |
| 44. C17×#120 | C2×C4 | semidirect |
| 52. C2×C22⋊Dic17 | D4 | semidirect |
| 69. C2×C4⋊Dic17 | D4 | semidirect |
| 72. C2×C4×Dic17 | D4 | semidirect |
| 73. C17×#99 | C2×C4 | semidirect |
| 83. C24×C17 | C22×C4 | semidirect |
| 124. C22⋊C4×C17 | C22×C4 | semidirect |
| 159. C23×C17 | C4×D4 | semidirect |
| 174. C2×C4×C17 | C4×D4 | semidirect |
| 229. Dic17 | B(4,𝔽2) | direct (N × H) |
| 240. B(4,𝔽2) | Dic17 | direct (N × H) |
| 260. H(5,𝔽2) | C2×Dic17 | semidirect |
| 273. #120 | C2×Dic17 | semidirect |
| 303. #99 | C2×Dic17 | semidirect |
| 307. C17 | C4×B(4,𝔽2) | semidirect |
| 314. C24 | C22×Dic17 | semidirect |
| 365. C22⋊C4 | C22×Dic17 | semidirect |
| 388. C23 | D4×Dic17 | semidirect |
| 423. C2×C4 | D4×Dic17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(5,𝔽2)×Dic17 | 2 |
| #120×Dic17 | 2 |
| #14529193 | 2 |
| #14529067 | 2 |
| #14528732 | 2 |
| #99×Dic17 | 2 |
| C2×C17×B(4,𝔽2) | 2 |
| C4×B(4,𝔽2) | 17 |