Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
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)×Dic13 | C2 | semidirect |
| 2. #120×Dic13 | C2 | semidirect |
| 3. #13115245 | C2 | semidirect |
| 4. #13115119 | C2 | semidirect |
| 5. #13114784 | C2 | semidirect |
| 6. #99×Dic13 | C2 | semidirect |
| 9. C24×Dic13 | C22 | semidirect |
| 18. C13×B(4,𝔽2) | C4 | semidirect |
| 20. #11718908 | C22 | semidirect |
| 25. #11718611 | C22 | semidirect |
| 27. C22⋊C4×Dic13 | C22 | semidirect |
| 28. #11718119 | C22 | semidirect |
| 31. C13×H(5,𝔽2) | C2×C4 | semidirect |
| 40. C23×Dic13 | D4 | semidirect |
| 44. C13×#120 | C2×C4 | semidirect |
| 52. C2×C22⋊Dic13 | D4 | semidirect |
| 69. C2×C4⋊Dic13 | D4 | semidirect |
| 72. C2×C4×Dic13 | D4 | semidirect |
| 73. C13×#99 | C2×C4 | semidirect |
| 84. C24×C13 | C22×C4 | semidirect |
| 125. C13×C22⋊C4 | C22×C4 | semidirect |
| 166. C23×C13 | C4×D4 | semidirect |
| 181. C2×C4×C13 | C4×D4 | semidirect |
| 212. B(4,𝔽2) | Dic13 | direct (N × H) |
| 250. Dic13 | B(4,𝔽2) | direct (N × H) |
| 253. H(5,𝔽2) | C2×Dic13 | semidirect |
| 266. #120 | C2×Dic13 | semidirect |
| 296. #99 | C2×Dic13 | semidirect |
| 313. C24 | C22×Dic13 | semidirect |
| 364. C22⋊C4 | C22×Dic13 | semidirect |
| 369. C13 | C4×B(4,𝔽2) | semidirect |
| 388. C23 | D4×Dic13 | semidirect |
| 423. C2×C4 | D4×Dic13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(5,𝔽2)×Dic13 | 2 |
| #120×Dic13 | 2 |
| #13115245 | 2 |
| #13115119 | 2 |
| #13114784 | 2 |
| #99×Dic13 | 2 |
| C2×C13×B(4,𝔽2) | 2 |
| C4×B(4,𝔽2) | 13 |