Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
240 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 69 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. #20276938 | C2 | semidirect |
| 2. D4×#11719908 | C2 | semidirect |
| 3. #20274104 | C2 | semidirect |
| 4. #20272786 | C2 | semidirect |
| 5. #20272771 | C2 | semidirect |
| 6. #20272761 | C2 | semidirect |
| 136. C53 | #12467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276938 | 2 |
| D4×#11719908 | 2 |
| #20274104 | 2 |
| #20272786 | 2 |
| #20272771 | 2 |
| #20272761 | 2 |
| C53×#1667 | 2 |
| #12467 | 53 |