Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
244 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 88 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. #20291099 | C2 | semidirect |
| 2. D4×#11719910 | C2 | semidirect |
| 3. #20289744 | C2 | semidirect |
| 4. D4⋊#11719910 | C2 | semidirect |
| 5. D4⋊#11719910 | C2 | semidirect |
| 6. #20289627 | C2 | semidirect |
| 70. #11719910 | D8 | semidirect |
| 76. D4×C53 | M32 | semidirect |
| 136. C53 | #12038 | semidirect |
| 190. D4 | #13133291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291099 | 2 |
| D4×#11719910 | 2 |
| #20289744 | 2 |
| D4⋊#11719910 | 2 |
| #20289627 | 2 |
| D8×#88322 | 2 |
| #12038 | 53 |