Finite Group DatabasebetaFinite Group DatabasebetaOrder 11760.
368 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 58 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×#15668767 | C2 | semidirect |
| 3. C7×(C2×D7)⋊AGL(1,𝔽5) | C3 | semidirect |
| 4. C2×AGL(1,𝔽5)×#3861 | C2 | semidirect |
| 7. C2×C5⋊#64423 | C4 | semidirect |
| 8. C2×C5×#64423 | C4 | semidirect |
| 14. C2×C7×C7⋊AGL(1,𝔽5) | C2×C3 | semidirect |
| 15. C2×C72×AGL(1,𝔽5) | C2×C3 | semidirect |
| 26. C2×C7×D35 | C3×C4 | semidirect |
| 28. C2×C5×C7×D7 | C3×C4 | semidirect |
| 41. C5×#3861 | C22⋊C4 | semidirect |
| 46. C2×#64423 | AGL(1,𝔽5) | semidirect |
| 50. (C2×D7)⋊AGL(1,𝔽5) | ΓL(1,𝔽8) | semidirect |
| 85. C2×C7⋊AGL(1,𝔽5) | C2×ΓL(1,𝔽8) | semidirect |
| 88. C2×C7×AGL(1,𝔽5) | AGL(1,𝔽7) | semidirect |
| 89. C2×C7×AGL(1,𝔽5) | C2×ΓL(1,𝔽8) | semidirect |
| 90. C5×C72 | C3×C22⋊C4 | semidirect |
| 109. C2×C7×D7 | C3×AGL(1,𝔽5) | semidirect |
| 119. #3861 | C22⋊AGL(1,𝔽5) | semidirect |
| 121. C2×D35 | C4×ΓL(1,𝔽8) | semidirect |
| 128. C2×C5×D7 | C4×ΓL(1,𝔽8) | semidirect |
| 195. C72 | C3×C22⋊AGL(1,𝔽5) | semidirect |
| 212. C2×AGL(1,𝔽5) | #64423 | semidirect |
| 214. C5×C7 | (C2×AGL(1,𝔽7))⋊C4 | semidirect |
| 215. C5×C7 | C22⋊C4×ΓL(1,𝔽8) | semidirect |
| 231. C2×D7 | AGL(1,𝔽5)×ΓL(1,𝔽8) | semidirect |
| 282. C7 | (C2×AGL(1,𝔽5))⋊AGL(1,𝔽7) | semidirect |
| 283. C7 | ΓL(1,𝔽8)×C22⋊AGL(1,𝔽5) | semidirect |
| 289. C5 | #72214763 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668767 | 2 |
| C2×D5×#64423 | 2 |
| C7×(C2×D7)⋊AGL(1,𝔽5) | 3 |
| C2×AGL(1,𝔽5)×#3861 | 2 |
| #72214763 | 5 |
| ΓL(1,𝔽8)×C22⋊AGL(1,𝔽5) | 7 |
| (C2×AGL(1,𝔽5))⋊AGL(1,𝔽7) | 7 |