Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
204 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 61 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. #20268168 | C2 | semidirect |
| 2. #20267986 | C2 | semidirect |
| 3. #20267544 | C2 | semidirect |
| 4. #20267534 | C2 | semidirect |
| 5. C8×D4×C103 | C2 | semidirect |
| 36. D4×C103 | D8 | semidirect |
| 50. C8×C103 | D8 | semidirect |
| 71. C103 | #1667 | semidirect |
| 74. C8×D4 | D103 | semidirect |
| 112. D4 | D824 | semidirect |
| 122. C8 | #13110090 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268168 | 2 |
| #20267986 | 2 |
| #20267544 | 2 |
| #20267534 | 2 |
| C8×D4×C103 | 2 |
| #1667 | 103 |