Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
398 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20276965 | C2 | semidirect |
| 2. #20276964 | C2 | semidirect |
| 3. #20274329 | C2 | semidirect |
| 4. C16×#88322 | C2 | semidirect |
| 5. C53×#2246 | C2 | semidirect |
| 42. C16×C53 | D8 | semidirect |
| 43. #11719908 | D8 | semidirect |
| 56. #88322 | D16 | semidirect |
| 68. #2246 | D53 | semidirect |
| 84. C53 | #12515 | semidirect |
| 113. C16 | #11719922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276965 | 2 |
| #20276964 | 2 |
| #20274329 | 2 |
| C16×#88322 | 2 |
| C53×#2246 | 2 |
| #12515 | 53 |