Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
396 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 396 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×D4 | C2 | semidirect |
| 2. C2×#66632 | C2 | semidirect |
| 3. #10621022 | C2 | semidirect |
| 4. C2×#66562 | C2 | semidirect |
| 5. C3×#6406 | C2 | semidirect |
| 6. #10620501 | C2 | semidirect |
| 7. (C2×D3)⋊(C7⋊C8) | C2 | semidirect |
| 11. C2×D84 | C22 | semidirect |
| 19. C2×C3⋊(C7⋊C8) | C22 | semidirect |
| 20. C3×C4⋊Dic7 | C22 | semidirect |
| 21. C2×C3×C7⋊C8 | C22 | semidirect |
| 29. #6406 | D3 | semidirect |
| 40. C3×C7×D4 | D4 | semidirect |
| 47. C7×D12 | D4 | semidirect |
| 66. C4⋊Dic7 | C2×D3 | semidirect |
| 68. C2×C7⋊C8 | C2×D3 | semidirect |
| 69. C2×D3×D4 | D7 | semidirect |
| 89. C2×D3×C7 | D8 | semidirect |
| 106. C7×D4 | D12 | semidirect |
| 172. C3×D4 | C22⋊D7 | semidirect |
| 181. D12 | C22⋊D7 | semidirect |
| 186. C3×C7 | #447 | semidirect |
| 222. C2×D3 | #1141 | semidirect |
| 241. D4 | #4247 | semidirect |
| 249. C7 | #4773 | semidirect |
| 275. C3 | #89989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C7×D4 | 2 |
| C2×#66632 | 2 |
| #10621022 | 2 |
| C2×#66562 | 2 |
| C3×#6406 | 2 |
| #10620501 | 2 |
| (C2×D3)⋊(C7⋊C8) | 2 |
| #89989 | 3 |
| #4773 | 7 |