Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
244 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 78 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×C7×ΓL(1,𝔽25) | C2 | semidirect |
| 3. C2×#66559 | C2 | semidirect |
| 4. #10620659 | C2 | semidirect |
| 5. C3×Dic7⋊C8 | C2 | semidirect |
| 6. (C2×D3)⋊(C7⋊C8) | C2 | semidirect |
| 7. C3⋊C8×Dic7 | C2 | semidirect |
| 27. Dic7⋊C8 | D3 | semidirect |
| 45. C7×C3⋊C8 | D4 | semidirect |
| 60. C2×ΓL(1,𝔽25) | D7 | semidirect |
| 77. C3×Dic7 | M16 | semidirect |
| 133. Dic7 | ΓL(1,𝔽25) | semidirect |
| 149. C3⋊C8 | C22⋊D7 | semidirect |
| 150. C3×C7 | #436 | semidirect |
| 198. C7 | #4838 | semidirect |
| 217. C3 | #89900 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×ΓL(1,𝔽25) | 2 |
| C4×#4247 | 2 |
| C2×#66559 | 2 |
| #10620659 | 2 |
| C3×Dic7⋊C8 | 2 |
| (C2×D3)⋊(C7⋊C8) | 2 |
| C3⋊C8×Dic7 | 2 |
| #89900 | 3 |
| #4838 | 7 |