Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
236 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 76 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. #20291101 | C2 | semidirect |
| 2. #20291099 | C2 | semidirect |
| 3. #20289738 | C2 | semidirect |
| 4. #20289666 | C2 | semidirect |
| 5. D4⋊#11719910 | C2 | semidirect |
| 6. #20289630 | C2 | semidirect |
| 91. #88322 | M32 | semidirect |
| 136. C53 | #12064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291101 | 2 |
| #20291099 | 2 |
| #20289738 | 2 |
| #20289666 | 2 |
| D4⋊#11719910 | 2 |
| #20289630 | 2 |
| #20273507 | 2 |
| #12064 | 53 |