Finite Group DatabasebetaFinite Group DatabasebetaOrder 13504.
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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. C2×#16809949 | C2 | semidirect |
| 2. C2×#16809946 | C2 | semidirect |
| 4. #20269910 | C2 | semidirect |
| 5. #20269901 | C2 | semidirect |
| 6. #20269897 | C2 | semidirect |
| 7. C22⋊Q8×C211 | C2 | semidirect |
| 27. C211⋊C8 | D4 | semidirect |
| 55. C211 | #468 | semidirect |
| 59. C22⋊Q8 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16809949 | 2 |
| C2×#16809946 | 2 |
| #20269951 | 2 |
| #20269910 | 2 |
| #20269901 | 2 |
| #20269897 | 2 |
| C22⋊Q8×C211 | 2 |
| #468 | 211 |