Finite Group DatabasebetaFinite Group DatabasebetaOrder 7056.
308 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 62 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. #72245283 | C2 | semidirect |
| 2. #72245248 | C3 | semidirect |
| 3. #72245198 | C3 | semidirect |
| 4. #72228714 | C3 | semidirect |
| 5. #72222014 | C2 | semidirect |
| 6. D4×ΓL(1,𝔽8)2 | C2 | semidirect |
| 10. D4×#3862 | C2×C3 | semidirect |
| 11. D4×#3861 | C2×C3 | semidirect |
| 12. C7×D4×ΓL(1,𝔽8) | C2×C3 | semidirect |
| 13. C4⋊#64425 | C2×C3 | semidirect |
| 14. C4⋊#64424 | C2×C3 | semidirect |
| 15. C4⋊(ΓL(1,𝔽8)⋊D7) | C2×C3 | semidirect |
| 16. #11924149 | C2×C3 | semidirect |
| 17. #11924148 | C2×C3 | semidirect |
| 18. ΓL(1,𝔽8)⋊(C7⋊C8) | C2×C3 | semidirect |
| 23. #11716071 | C32 | semidirect |
| 36. ΓL(1,𝔽8)2 | D8 | semidirect |
| 37. C72×D4 | C2×C32 | semidirect |
| 38. C4⋊(C7⋊D7) | C2×C32 | semidirect |
| 39. C7⋊(C7⋊C8) | C2×C32 | semidirect |
| 65. D4×ΓL(1,𝔽8) | AGL(1,𝔽7) | semidirect |
| 75. #3862 | C3×D8 | semidirect |
| 76. #3861 | C3×D8 | semidirect |
| 77. C7×ΓL(1,𝔽8) | C3×D8 | semidirect |
| 107. C7×D4 | C3×AGL(1,𝔽7) | semidirect |
| 112. C72 | C32×D8 | semidirect |
| 153. ΓL(1,𝔽8) | #1141⋊C3 | semidirect |
| 175. D4 | ΓL(1,𝔽8)⋊AGL(1,𝔽7) | semidirect |
| 178. C7 | C3×#1141⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72245283 | 2 |
| #72245248 | 3 |
| #72245198 | 3 |
| #72228714 | 3 |
| #72222014 | 2 |
| D4×ΓL(1,𝔽8)2 | 2 |
| C3×#1141⋊C3 | 7 |