Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
252 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 4. #10620653 | C2 | semidirect |
| 5. C7×Dic3⋊C8 | C2 | semidirect |
| 6. Dic3⋊(C7⋊C8) | C2 | semidirect |
| 7. #10620518 | C2 | semidirect |
| 64. Dic3⋊C8 | D7 | semidirect |
| 72. Dic21 | M16 | semidirect |
| 75. C7×Dic3 | M16 | semidirect |
| 142. C3×C7 | #423 | semidirect |
| 170. Dic3 | #1131 | semidirect |
| 186. C7 | #5118 | semidirect |
| 202. C3 | #89609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1131 | 2 |
| C4×Dic3×D7 | 2 |
| C2×#66557 | 2 |
| #10620653 | 2 |
| C7×Dic3⋊C8 | 2 |
| Dic3⋊(C7⋊C8) | 2 |
| #10620518 | 2 |
| #89609 | 3 |
| #5118 | 7 |