Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
650 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 84 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. #20291154 | C2 | semidirect |
| 2. #20290878 | C2 | semidirect |
| 3. #20290106 | C2 | semidirect |
| 4. #20290055 | C2 | semidirect |
| 5. #20289602 | C2 | semidirect |
| 6. #20289567 | C2 | semidirect |
| 25. #16810910 | C4 | semidirect |
| 26. #16810819 | C4 | semidirect |
| 27. #16810818 | C4 | semidirect |
| 32. C53×#476 | C4 | semidirect |
| 58. #13133214 | C2×C4 | semidirect |
| 73. C4⋊#88322 | C2×C4 | semidirect |
| 79. C4⋊Q8×C53 | C2×C4 | semidirect |
| 82. C4⋊C8×C53 | C2×C4 | semidirect |
| 163. D4×C53 | #104 | semidirect |
| 183. D212 | #104 | semidirect |
| 247. #476 | #6157 | semidirect |
| 267. C53 | #9325 | semidirect |
| 275. C4⋊Q8 | C2×#6157 | semidirect |
| 302. C4⋊C8 | C2×#6157 | semidirect |
| 397. D4 | #13133282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291154 | 2 |
| #20290878 | 2 |
| #20290106 | 2 |
| #20290055 | 2 |
| #20289602 | 2 |
| #20289567 | 2 |
| #20284808 | 2 |
| #9325 | 53 |