Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 70 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×D21 | C2 | semidirect |
| 2. C2×C3×#1143 | C2 | semidirect |
| 4. C2×#66565 | C2 | semidirect |
| 5. C7×#835 | C2 | semidirect |
| 6. #10620510 | C2 | semidirect |
| 7. #10620492 | C2 | semidirect |
| 25. C2×#1143 | D3 | semidirect |
| 35. C3×C7×Q8 | D4 | semidirect |
| 45. Dic42 | D4 | semidirect |
| 71. #835 | D7 | semidirect |
| 77. C2×D21 | SD16 | semidirect |
| 91. C7×Q8 | #67 | semidirect |
| 151. C3×Q8 | D28 | semidirect |
| 168. C3×C7 | #448 | semidirect |
| 208. Q8 | #4246 | semidirect |
| 222. C7 | #5170 | semidirect |
| 241. C3 | #89578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D21 | 2 |
| C2×C3×#1143 | 2 |
| #10621027 | 2 |
| C2×#66565 | 2 |
| C7×#835 | 2 |
| #10620510 | 2 |
| #10620492 | 2 |
| #89578 | 3 |
| #5170 | 7 |