Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
244 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 76 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×#66557 | C2 | semidirect |
| 4. #10620653 | C2 | semidirect |
| 5. C3×(C2×D7)⋊C8 | C2 | semidirect |
| 6. (C2×D3)⋊(C7⋊C8) | C2 | semidirect |
| 7. #10620486 | C2 | semidirect |
| 26. (C2×D7)⋊C8 | D3 | semidirect |
| 45. C7×C3⋊C8 | D4 | semidirect |
| 61. C2×ΓL(1,𝔽25) | D7 | semidirect |
| 76. Dic21 | M16 | semidirect |
| 149. C3⋊C8 | C22⋊D7 | semidirect |
| 150. C3×C7 | #436 | semidirect |
| 198. C7 | #4729 | 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×#4245 | 2 |
| C2×#66557 | 2 |
| #10620653 | 2 |
| C3×(C2×D7)⋊C8 | 2 |
| (C2×D3)⋊(C7⋊C8) | 2 |
| #10620486 | 2 |
| #89900 | 3 |
| #4729 | 7 |