Finite Group DatabasebetaFinite Group DatabasebetaOrder 13504.
148 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 45 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. C2×#16809952 | C2 | semidirect |
| 4. #20269902 | C2 | semidirect |
| 5. #20269901 | C2 | semidirect |
| 7. C2×Q16×C211 | C2 | semidirect |
| 45. C2×D211 | Q16 | semidirect |
| 57. C211 | #451 | semidirect |
| 61. C2×Q16 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D211 | 2 |
| C2×#16809952 | 2 |
| #20269953 | 2 |
| #20269902 | 2 |
| #20269901 | 2 |
| (C2×D211)⋊C8 | 2 |
| C2×Q16×C211 | 2 |
| #451 | 211 |