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×C7×#215 | C2 | semidirect |
| 4. C2×#66567 | C2 | semidirect |
| 5. C3×#6409 | C2 | semidirect |
| 6. #10620509 | C2 | semidirect |
| 7. #10620492 | C2 | semidirect |
| 28. #6409 | D3 | semidirect |
| 35. C3×C7×Q8 | D4 | semidirect |
| 45. Dic42 | D4 | semidirect |
| 68. C2×#215 | D7 | semidirect |
| 77. C2×D21 | SD16 | semidirect |
| 91. C7×Q8 | D12 | semidirect |
| 151. C3×Q8 | C22⋊D7 | semidirect |
| 168. C3×C7 | #448 | semidirect |
| 208. Q8 | #4247 | semidirect |
| 222. C7 | #4806 | semidirect |
| 241. C3 | #89942 | 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×C7×#215 | 2 |
| #10621028 | 2 |
| C2×#66567 | 2 |
| C3×#6409 | 2 |
| #10620509 | 2 |
| #10620492 | 2 |
| #89942 | 3 |
| #4806 | 7 |