Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
284 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 284 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. #10621427 | C2 | semidirect |
| 2. C2×C7×#215 | C2 | semidirect |
| 3. C2×C3×#1143 | C2 | semidirect |
| 5. C2×#66567 | C2 | semidirect |
| 6. C2×#66565 | C2 | semidirect |
| 7. #10620486 | C2 | semidirect |
| 24. C2×#1143 | D3 | semidirect |
| 45. C3×C7⋊C8 | D4 | semidirect |
| 46. C7×C3⋊C8 | D4 | semidirect |
| 62. C2×#215 | D7 | semidirect |
| 76. Dic21 | SD16 | semidirect |
| 94. C7⋊C8 | #67 | semidirect |
| 145. C3⋊C8 | C22⋊D7 | semidirect |
| 146. C3×C7 | #492 | semidirect |
| 191. C7 | #5175 | semidirect |
| 206. C3 | #89947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621427 | 2 |
| C2×C7×#215 | 2 |
| C2×C3×#1143 | 2 |
| #10621025 | 2 |
| C2×#66567 | 2 |
| C2×#66565 | 2 |
| #10620486 | 2 |
| #89947 | 3 |
| #5175 | 7 |