Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
252 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 86 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. C7×Dic3⋊C8 | C2 | semidirect |
| 5. C3×Dic7⋊C8 | C2 | semidirect |
| 6. Dic3⋊(C7⋊C8) | C2 | semidirect |
| 7. Dic7⋊(C3⋊C8) | C2 | semidirect |
| 27. Dic7⋊C8 | D3 | semidirect |
| 63. Dic3⋊C8 | D7 | semidirect |
| 73. C3×Dic7 | M16 | semidirect |
| 75. C7×Dic3 | M16 | semidirect |
| 126. Dic7 | ΓL(1,𝔽25) | semidirect |
| 142. C3×C7 | #423 | semidirect |
| 170. Dic3 | #1131 | semidirect |
| 186. C7 | #4837 | 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×#66622 | 2 |
| C4×D21⋊C4 | 2 |
| C2×#66559 | 2 |
| C7×Dic3⋊C8 | 2 |
| C3×Dic7⋊C8 | 2 |
| Dic3⋊(C7⋊C8) | 2 |
| Dic7⋊(C3⋊C8) | 2 |
| #89609 | 3 |
| #4837 | 7 |