Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20268591 | C2 | semidirect |
| 2. C2×#15693049 | C2 | semidirect |
| 3. #20268360 | C2 | semidirect |
| 4. #20267807 | C2 | semidirect |
| 5. #20267797 | C2 | semidirect |
| 6. #20267764 | C2 | semidirect |
| 7. #344×C103 | C2 | semidirect |
| 41. C2×Dic206 | D4 | semidirect |
| 50. C2×D412 | D4 | semidirect |
| 69. M16×C103 | D4 | semidirect |
| 71. C2×C8×C103 | D4 | semidirect |
| 143. C103 | #2008 | semidirect |
| 150. #344 | D103 | semidirect |
| 208. M16 | D412 | semidirect |
| 210. C2×C8 | D412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268591 | 2 |
| C2×#15693049 | 2 |
| #20268360 | 2 |
| #20267807 | 2 |
| #20267797 | 2 |
| #20267764 | 2 |
| #344×C103 | 2 |
| #2008 | 103 |