Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
216 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 216 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 | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C13 | C32×C4 |
| prime radical | D13⋊C3×#3861 | C2 |
| cosocle | C72×D13 | C2×C32 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #21439627 | C3 | semidirect |
| 3. #21439624 | C3 | semidirect |
| 4. #21439623 | C3 | semidirect |
| 5. C7×#11763979 | C3 | semidirect |
| 6. C13⋊C3×#3861 | C4 | semidirect |
| 13. C7×C7⋊#261 | C32 | semidirect |
| 14. #14274263 | C3×C4 | semidirect |
| 15. #14274262 | C3×C4 | semidirect |
| 16. C13×#3861 | C3×C4 | semidirect |
| 17. C72×C13⋊C3 | C3×C4 | semidirect |
| 29. #11763979 | ΓL(1,𝔽8) | semidirect |
| 35. C72×C13 | C32×C4 | semidirect |
| 54. C7⋊#261 | C3×ΓL(1,𝔽8) | semidirect |
| 67. C7×C13⋊C3 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 68. C7×C13⋊C3 | C4×ΓL(1,𝔽8) | semidirect |
| 86. #3861 | AGL(1,𝔽13) | semidirect |
| 93. C7×C13 | C3×ΓL(1,𝔽8)⋊C4 | semidirect |
| 94. C7×C13 | C3×C4×ΓL(1,𝔽8) | semidirect |
| 111. C72 | C3×AGL(1,𝔽13) | semidirect |
| 127. C13⋊C3 | #10596873 | semidirect |
| 148. C13 | C3×#10596873 | semidirect |
| 155. C7 | ΓL(1,𝔽8)⋊AGL(1,𝔽13) | semidirect |
| 156. C7 | ΓL(1,𝔽8)×AGL(1,𝔽13) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13⋊C3×#3861 | 2 |
| #21439627 | 3 |
| #21439624 | 3 |
| #21439623 | 3 |
| C7×#11763979 | 3 |
| ΓL(1,𝔽8)×AGL(1,𝔽13) | 7 |
| ΓL(1,𝔽8)⋊AGL(1,𝔽13) | 7 |
| C3×#10596873 | 13 |