Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
226 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 53 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×Q16×D107 | C2 | semidirect |
| 2. C2×#16812054 | C2 | semidirect |
| 3. C2×#16812052 | C2 | semidirect |
| 5. #20292430 | C2 | semidirect |
| 6. (C2×D107)⋊C16 | C2 | semidirect |
| 7. #358×C107 | C2 | semidirect |
| 32. Dic428 | D4 | semidirect |
| 43. Q16×C107 | D4 | semidirect |
| 74. C2×D107 | SD32 | semidirect |
| 87. C107 | #2185 | semidirect |
| 93. #358 | D107 | semidirect |
| 123. Q16 | D428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D107 | 2 |
| C2×#16812054 | 2 |
| C2×#16812052 | 2 |
| #20292864 | 2 |
| #20292430 | 2 |
| (C2×D107)⋊C16 | 2 |
| #358×C107 | 2 |
| #2185 | 107 |