Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
156 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 39 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 | #64423⋊D13 |
| commutator, hypocenter | C72×C13 | C22×C9 |
| Fitting, socle, cosocle | C3×C72×C13 | C22×C3 |
| prime radical | C3×D7×D91 | C3 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26039458 | C2 | semidirect |
| 2. C13×#11725076 | C2 | semidirect |
| 3. #26039448 | C2 | semidirect |
| 5. C13×#89204 | C22 | semidirect |
| 11. D7×D91 | C9 | semidirect |
| 22. C7⋊D91 | C2×C9 | semidirect |
| 23. C7×D91 | C2×C9 | semidirect |
| 24. C7×C13×D7 | C2×C9 | semidirect |
| 29. #11725076 | D13 | semidirect |
| 34. C72×C13 | C22×C9 | semidirect |
| 45. #89204 | C2×D13 | semidirect |
| 66. D91 | D7⋊C9 | semidirect |
| 68. C13×D7 | D7⋊C9 | semidirect |
| 82. C7×D7 | C9×D13 | semidirect |
| 85. C7×C13 | C2×D7⋊C9 | semidirect |
| 86. C7×C13 | C2×D7⋊C9 | semidirect |
| 97. C72 | C2×C9×D13 | semidirect |
| 127. D7 | (C7⋊C9)⋊D13 | semidirect |
| 128. C13 | #11725076⋊C2 | semidirect |
| 133. C7 | D13×D7⋊C9 | semidirect |
| 134. C7 | C2×(C7⋊C9)⋊D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26039458 | 2 |
| C13×#11725076 | 2 |
| #26039448 | 2 |
| C3×D7×D91 | 3 |
| C2×(C7⋊C9)⋊D13 | 7 |
| D13×D7⋊C9 | 7 |
| #11725076⋊C2 | 13 |