Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
128 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 37 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 | C3 | #21439622 |
| commutator, hypocenter | C72×C13 | C22×C9 |
| Fitting, socle, cosocle | C3×C72×C13 | C22×C3 |
| prime radical | C3×(C7⋊D7)⋊D13 | C3 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26039464 | C2 | semidirect |
| 2. #26039464 | C2 | semidirect |
| 3. C13×#11725078 | C2 | semidirect |
| 5. C13×#89205 | C22 | semidirect |
| 11. (C7⋊D7)⋊D13 | C9 | semidirect |
| 20. C13×C7⋊D7 | C2×C9 | semidirect |
| 21. C7×D91 | C2×C9 | semidirect |
| 22. C7×D91 | C2×C9 | semidirect |
| 25. #11725078 | D13 | semidirect |
| 30. C72×C13 | C22×C9 | semidirect |
| 40. #89205 | C2×D13 | semidirect |
| 55. D91 | D7⋊C9 | semidirect |
| 56. D91 | D7⋊C9 | semidirect |
| 71. C7⋊D7 | C9×D13 | semidirect |
| 75. C7×C13 | C2×D7⋊C9 | semidirect |
| 76. C7×C13 | C2×D7⋊C9 | semidirect |
| 85. C72 | C2×C9×D13 | semidirect |
| 113. C13 | #11725075⋊C2 | semidirect |
| 117. C7 | D13×D7⋊C9 | semidirect |
| 118. C7 | D13×D7⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26039464 | 2 |
| C13×#11725078 | 2 |
| C3×(C7⋊D7)⋊D13 | 3 |
| D13×D7⋊C9 | 7 |
| #11725075⋊C2 | 13 |