Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
396 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 396 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×D3×D28 | C2 | semidirect |
| 2. C7×#895 | C2 | semidirect |
| 3. C2×#66562 | C2 | semidirect |
| 4. C2×#66560 | C2 | semidirect |
| 5. #10620648 | C2 | semidirect |
| 6. C3×#6383 | C2 | semidirect |
| 7. (C2×D3)⋊(C7⋊C8) | C2 | semidirect |
| 12. C2×C7×D12 | C22 | semidirect |
| 18. C3×C7×C4⋊C4 | C22 | semidirect |
| 19. C2×C3⋊(C7⋊C8) | C22 | semidirect |
| 21. C2×C3×C7⋊C8 | C22 | semidirect |
| 30. #6383 | D3 | semidirect |
| 42. D84 | D4 | semidirect |
| 50. C3×D28 | D4 | semidirect |
| 63. C7×C4⋊C4 | C2×D3 | semidirect |
| 68. C2×C7⋊C8 | C2×D3 | semidirect |
| 72. #895 | D7 | semidirect |
| 85. C2×D3×C7 | D8 | semidirect |
| 114. D28 | D12 | semidirect |
| 124. C2×D12 | C2×D7 | semidirect |
| 127. C3×C4⋊C4 | C2×D7 | semidirect |
| 186. C3×C7 | #447 | semidirect |
| 200. C4⋊C4 | D3×D7 | semidirect |
| 222. C2×D3 | #1141 | semidirect |
| 249. C7 | #4773 | semidirect |
| 275. C3 | #89808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×D28 | 2 |
| C7×#895 | 2 |
| C2×#66562 | 2 |
| C2×#66560 | 2 |
| #10620648 | 2 |
| C3×#6383 | 2 |
| (C2×D3)⋊(C7⋊C8) | 2 |
| #89808 | 3 |
| #4773 | 7 |