Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
152 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 22 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C19×#3862 | C22×C3 |
| Fitting, socle | C72×C19 | C2×C3×D3 |
| LCS | G ▷ C19×#3862 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #30660729 | C2 | semidirect |
| 2. C19×#64418⋊C3 | C2 | semidirect |
| 3. ΓL(1,𝔽8)⋊(ΓL(1,𝔽8)⋊D19) | C2 | semidirect |
| 4. #64418⋊D19 | C3 | semidirect |
| 6. C19×ΓL(1,𝔽8)2 | C22 | semidirect |
| 7. C19⋊#64418 | C2×C3 | semidirect |
| 8. C19×#64418 | C2×C3 | semidirect |
| 12. #19150292 | C2×C3 | semidirect |
| 13. #19150288 | D3 | semidirect |
| 15. C19×#3862 | C22×C3 | semidirect |
| 16. C19×#3861 | C2×D3 | semidirect |
| 19. C7⋊D133 | C3×D3 | semidirect |
| 26. C72×C19 | C2×C3×D3 | semidirect |
| 29. #64418⋊C3 | D19 | semidirect |
| 45. ΓL(1,𝔽8)2 | C2×D19 | semidirect |
| 61. #64418 | C3×D19 | semidirect |
| 73. #3862 | C2×C3×D19 | semidirect |
| 74. #3861 | D3×D19 | semidirect |
| 97. C72 | C3×D3×D19 | semidirect |
| 120. C19 | (#64418⋊C2)⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30660729 | 2 |
| C19×#64418⋊C3 | 2 |
| ΓL(1,𝔽8)⋊(ΓL(1,𝔽8)⋊D19) | 2 |
| #64418⋊D19 | 3 |
| #64423⋊D19 | 3 |
| (#64418⋊C2)⋊C3 | 19 |
| C3×D3×D19 | 49 |