Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
152 conjugacy classes of subgroups; only the 18 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 18 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, Fitting, socle, hypocenter | C3×C72×C13 | C3×C4 |
| prime radical | C3×#16838450 | C2 |
| cosocle | C3×C7⋊D91 | C2×C3 |
| LCS | G ▷ C3×C72×C13 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3⋊#14579330 | C3 | semidirect |
| 4. C3×C13×#3861 | C4 | semidirect |
| 9. C3×C72×C13 | C3×C4 | semidirect |
| 11. C13×#3861 | Dic3 | semidirect |
| 23. C72×C13 | C3×Dic3 | semidirect |
| 43. C3×#3861 | #261 | semidirect |
| 71. C3×C72 | C3×#261 | semidirect |
| 73. #3861 | C3⋊#261 | semidirect |
| 92. C72 | C3×C3⋊#261 | semidirect |
| 111. C3×C13 | #5997⋊C3 | semidirect |
| 135. C13 | C3⋊(#5997⋊C3) | semidirect |
| 149. C3 | #21439682 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16838450 | 2 |
| C3⋊#14579330 | 3 |
| #21439682 | 3 |
| C3⋊(#5997⋊C3) | 13 |
| C3×C3⋊#261 | 49 |