Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
284 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 74 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×#66634 | C2 | semidirect |
| 2. C7×#944 | C2 | semidirect |
| 3. C2×C3×#1143 | C2 | semidirect |
| 5. C2×#66568 | C2 | semidirect |
| 6. C2×#66563 | C2 | semidirect |
| 7. Dic3×C7⋊C8 | C2 | semidirect |
| 26. C2×#1143 | D3 | semidirect |
| 45. C3⋊(C7⋊C8) | D4 | semidirect |
| 46. C3×C7⋊C8 | D4 | semidirect |
| 61. #944 | D7 | semidirect |
| 76. C7×Dic3 | SD16 | semidirect |
| 94. C7⋊C8 | #67 | semidirect |
| 146. C3×C7 | #492 | semidirect |
| 173. Dic3 | #1143 | semidirect |
| 191. C7 | #5175 | semidirect |
| 206. C3 | #89857 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66634 | 2 |
| C7×#944 | 2 |
| C2×C3×#1143 | 2 |
| #10621020 | 2 |
| C2×#66568 | 2 |
| C2×#66563 | 2 |
| Dic3×C7⋊C8 | 2 |
| #89857 | 3 |
| #5175 | 7 |