Finite Group DatabasebetaFinite Group DatabasebetaOrder 13504.
158 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 158 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 |
|---|---|---|
| 1. C2×Q8×D211 | C2 | semidirect |
| 2. C2×#16809951 | C2 | semidirect |
| 3. C2×#16809949 | C2 | semidirect |
| 5. #20269900 | C2 | semidirect |
| 6. (C2×D211)⋊C8 | C2 | semidirect |
| 7. #103×C211 | C2 | semidirect |
| 27. Dic422 | D4 | semidirect |
| 38. Q8×C211 | D4 | semidirect |
| 49. C2×D211 | SD16 | semidirect |
| 61. C211 | #448 | semidirect |
| 68. #103 | D211 | semidirect |
| 91. Q8 | D844 | 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×#16809951 | 2 |
| C2×#16809949 | 2 |
| #20269952 | 2 |
| #20269900 | 2 |
| (C2×D211)⋊C8 | 2 |
| #103×C211 | 2 |
| #448 | 211 |