Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
396 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 79 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. C22×D84 | C2 | semidirect |
| 2. C3×C7×#121 | C2 | semidirect |
| 3. C2×#66632 | C2 | semidirect |
| 4. #10620669 | C2 | semidirect |
| 5. #10620648 | C2 | semidirect |
| 9. C2×C3×C7×D4 | C22 | semidirect |
| 14. C3×C7×C4⋊C4 | C22 | semidirect |
| 17. C2×C3⋊(C7⋊C8) | C22 | semidirect |
| 19. C7×#121 | D3 | semidirect |
| 38. D84 | D4 | semidirect |
| 42. C2×C7×D4 | C2×D3 | semidirect |
| 47. C7×C4⋊C4 | C2×D3 | semidirect |
| 52. C3×#121 | D7 | semidirect |
| 61. C22×C3×C7 | D8 | semidirect |
| 89. C2×C3×D4 | C2×D7 | semidirect |
| 94. C3×C4⋊C4 | C2×D7 | semidirect |
| 106. #121 | D21 | semidirect |
| 114. C22×C7 | #213 | semidirect |
| 139. C3×C7 | #447 | semidirect |
| 145. C2×D4 | C2×D21 | semidirect |
| 149. C4⋊C4 | C2×D21 | semidirect |
| 162. C22×C3 | #1141 | semidirect |
| 187. C7 | #5036 | semidirect |
| 203. C22 | #66632 | semidirect |
| 208. C3 | #89808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D84 | 2 |
| C3×C7×#121 | 2 |
| C2×#66632 | 2 |
| #10620669 | 2 |
| #10620648 | 2 |
| #89808 | 3 |
| #5036 | 7 |