Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
438 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20276344 | C2 | semidirect |
| 3. #20276325 | C2 | semidirect |
| 4. #20276320 | C2 | semidirect |
| 5. C53×#2153 | C2 | semidirect |
| 40. C2×#11719908 | D4 | semidirect |
| 136. #2153 | D53 | semidirect |
| 160. C53 | #13200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283411 | 2 |
| #20276344 | 2 |
| #20276325 | 2 |
| #20276320 | 2 |
| C53×#2153 | 2 |
| #13200 | 53 |