Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
360 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. #20276527 | C2 | semidirect |
| 3. #20272692 | C2 | semidirect |
| 4. #20272689 | C2 | semidirect |
| 5. C53×#1455 | C2 | semidirect |
| 14. #16810444 | C22 | semidirect |
| 20. C53×#322 | C22 | semidirect |
| 21. C82×C53 | C22 | semidirect |
| 74. Dic212 | M16 | semidirect |
| 76. D424 | M16 | semidirect |
| 123. #1455 | D53 | semidirect |
| 144. #322 | C2×D53 | semidirect |
| 145. C82 | C2×D53 | semidirect |
| 146. C53 | #11669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283626 | 2 |
| #20276527 | 2 |
| #20272692 | 2 |
| #20272689 | 2 |
| C53×#1455 | 2 |
| #11669 | 53 |