Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
146 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 146 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 | C3×C13×#3862 | C22 |
| Fitting, socle | C3×C72×C13 | C2×D3 |
| LCS | G ▷ C3×C13×#3862 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3⋊(C13⋊#64418) | C2 | semidirect |
| 2. D3×C13×#3862 | C2 | semidirect |
| 3. C3×C13⋊#64418 | C2 | semidirect |
| 6. C3×C13×#3862 | C22 | semidirect |
| 8. D3×C72×C13 | D3 | semidirect |
| 13. C13⋊#64418 | D3 | direct (N × H) |
| 15. C3×C72×C13 | C2×D3 | semidirect |
| 17. C13×#3862 | C2×D3 | semidirect |
| 25. D3×#3862 | D13 | semidirect |
| 29. C72×C13 | D32 | semidirect |
| 41. C3×#3862 | C2×D13 | semidirect |
| 45. D3×C72 | D39 | semidirect |
| 69. C3×C72 | C2×D39 | semidirect |
| 71. #3862 | D3×D13 | semidirect |
| 88. D3×C13 | #64418 | semidirect |
| 91. C72 | D3×D39 | semidirect |
| 102. C3×C13 | C2×#64418 | semidirect |
| 124. C13 | D3×#64418 | semidirect |
| 137. D3 | C13⋊#64418 | direct (N × H) |
| 141. C3 | C2×C13⋊#64418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊(C13⋊#64418) | 2 |
| D3×C13×#3862 | 2 |
| C3×C13⋊#64418 | 2 |
| D3×C7×D91 | 3 |
| C2×C13⋊#64418 | 3 |
| D3×#64418 | 13 |
| D3×D39 | 49 |