Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
480 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20276643 | C2 | semidirect |
| 2. #20276626 | C2 | semidirect |
| 3. #20275713 | C2 | semidirect |
| 4. #20272727 | C2 | semidirect |
| 5. #20272724 | C2 | semidirect |
| 6. #20272639 | C2 | semidirect |
| 7. C53×#3191 | C2 | semidirect |
| 43. C2×Q16×C53 | D4 | semidirect |
| 45. C2×D8×C53 | D4 | semidirect |
| 57. #107×C53 | D4 | semidirect |
| 58. #107×C53 | D4 | semidirect |
| 194. #3191 | D53 | semidirect |
| 228. C53 | #12104 | semidirect |
| 233. C2×Q16 | C22⋊D53 | semidirect |
| 238. C2×D8 | C22⋊D53 | semidirect |
| 258. #107 | C22⋊D53 | semidirect |
| 259. #107 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276643 | 2 |
| #20276626 | 2 |
| #20275713 | 2 |
| #20272727 | 2 |
| #20272724 | 2 |
| #20272639 | 2 |
| C53×#3191 | 2 |
| #12104 | 53 |