Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
238 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 238 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. #20291129 | C2 | semidirect |
| 3. #20289738 | C2 | semidirect |
| 4. #20289682 | C2 | semidirect |
| 6. C8×#11719910 | C2 | semidirect |
| 52. #11719923 | C16 | semidirect |
| 67. #11719910 | SD16 | semidirect |
| 80. Dic106 | C2×C16 | semidirect |
| 86. #88322 | C2×C16 | semidirect |
| 128. C53 | C16×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291129 | 2 |
| D4×#11719910 | 2 |
| #20289738 | 2 |
| #20289682 | 2 |
| D4⋊#11719910 | 2 |
| C8×#11719910 | 2 |
| #20273518 | 2 |
| C16×SD16 | 53 |