Finite Group DatabasebetaFinite Group Databasebeta← C11×C3⋊(C11⋊#1044) #49137807
Order 36300.
288 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 42 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 |
|---|---|---|
| 3. C3×C52×C112 | C4 | semidirect |
| 8. C3⋊(C11⋊#1044) | C11 | direct (N × H) |
| 10. C52×C112 | Dic3 | semidirect |
| 13. C3×C5×C112 | AGL(1,𝔽5) | semidirect |
| 23. C3×C52×C11 | Dic11 | semidirect |
| 24. C3×C52×C11 | C4×C11 | semidirect |
| 29. C5×C112 | ΓL(1,𝔽16) | semidirect |
| 34. C3×C112 | #1044 | semidirect |
| 43. C52×C11 | C11×Dic3 | semidirect |
| 44. C52×C11 | Dic33 | semidirect |
| 52. C3×C5×C11 | C11×AGL(1,𝔽5) | semidirect |
| 53. C3×C5×C11 | C11⋊AGL(1,𝔽5) | semidirect |
| 57. C112 | C3⋊#1044 | semidirect |
| 65. C3×C52 | C11×Dic11 | semidirect |
| 74. C5×C11 | C11×ΓL(1,𝔽16) | semidirect |
| 75. C5×C11 | C3⋊(C11⋊AGL(1,𝔽5)) | semidirect |
| 80. C3×C11 | C11×#1044 | semidirect |
| 81. C3×C11 | C11⋊#1044 | semidirect |
| 84. C52 | C11×Dic33 | semidirect |
| 90. C3×C5 | C11×C11⋊AGL(1,𝔽5) | semidirect |
| 93. C11 | C11×C3⋊#1044 | semidirect |
| 94. C11 | C3⋊(C11⋊#1044) | direct (N × H) |
| 99. C5 | C11×C3⋊(C11⋊AGL(1,𝔽5)) | semidirect |
| 101. C3 | C11×C11⋊#1044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C112×C5⋊D5 | 2 |
| C11×C11⋊#1044 | 3 |
| C11×C3⋊(C11⋊AGL(1,𝔽5)) | 5 |
| C3⋊(C11⋊#1044) | 11 |
| C11×C3⋊#1044 | 11 |