Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
232 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20276617 | C2 | semidirect |
| 4. #20272693 | C2 | semidirect |
| 6. #20272633 | C2 | semidirect |
| 7. C53×#1370 | C2 | semidirect |
| 60. #11719913 | C16 | semidirect |
| 80. Dic106 | C2×C16 | semidirect |
| 84. C8×C53 | C2×C16 | semidirect |
| 105. #1370 | D53 | semidirect |
| 128. C53 | SD16⋊C16 | semidirect |
| 192. C8 | C16×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276617 | 2 |
| #20276534 | 2 |
| C8×#11719913 | 2 |
| #20272693 | 2 |
| #20272669 | 2 |
| #20272633 | 2 |
| C53×#1370 | 2 |
| SD16⋊C16 | 53 |