Finite Group DatabasebetaFinite Group DatabasebetaOrder 13504.
218 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20269972 | C2 | semidirect |
| 2. #20269967 | C2 | semidirect |
| 3. #20269962 | C2 | semidirect |
| 4. #20269960 | C2 | semidirect |
| 5. #20269956 | C2 | semidirect |
| 6. #20269955 | C2 | semidirect |
| 8. C4×C22⋊D211 | C2 | semidirect |
| 9. C2×C4⋊C4×C211 | C2 | semidirect |
| 66. C211 | #539 | semidirect |
| 76. C2×C4⋊C4 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20269972 | 2 |
| #20269967 | 2 |
| #20269962 | 2 |
| #20269960 | 2 |
| #20269956 | 2 |
| #20269955 | 2 |
| #20269951 | 2 |
| C4×C22⋊D211 | 2 |
| C2×C4⋊C4×C211 | 2 |
| #539 | 211 |