Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 76 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×D3×C7×Q8 | C2 | semidirect |
| 2. C2×#66634 | C2 | semidirect |
| 4. C2×#66568 | C2 | semidirect |
| 5. C3×#6409 | C2 | semidirect |
| 6. #10620507 | C2 | semidirect |
| 7. (C2×D3)⋊(C7⋊C8) | C2 | semidirect |
| 29. #6409 | D3 | semidirect |
| 35. C3×C7×Q8 | D4 | semidirect |
| 47. C7×Dic6 | D4 | semidirect |
| 67. C2×D3×Q8 | D7 | semidirect |
| 80. C2×D3×C7 | SD16 | semidirect |
| 94. C7×Q8 | D12 | semidirect |
| 151. C3×Q8 | C22⋊D7 | semidirect |
| 165. Dic6 | C22⋊D7 | semidirect |
| 168. C3×C7 | #448 | semidirect |
| 195. C2×D3 | #1143 | semidirect |
| 208. Q8 | #4247 | semidirect |
| 222. C7 | #4806 | semidirect |
| 241. C3 | #89999 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C7×Q8 | 2 |
| C2×#66634 | 2 |
| #10621022 | 2 |
| C2×#66568 | 2 |
| C3×#6409 | 2 |
| #10620507 | 2 |
| (C2×D3)⋊(C7⋊C8) | 2 |
| #89999 | 3 |
| #4806 | 7 |