Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
152 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 40 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 | C2 | #26039534 |
| commutator, hypocenter | C72×C13 | C32×C4 |
| Fitting, socle, cosocle | C2×C72×C13 | C2×C32 |
| prime radical | C2×#19153212 | C2 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #21439556 | C3 | semidirect |
| 3. #21439542 | C3 | semidirect |
| 4. #21439532 | C3 | semidirect |
| 5. C7×#11763964 | C3 | semidirect |
| 6. #19153212 | C4 | semidirect |
| 13. C7×Dic91 | C32 | semidirect |
| 14. C13×#3862 | C3×C4 | semidirect |
| 15. #14274263 | C3×C4 | semidirect |
| 16. C7×#63271 | C3×C4 | semidirect |
| 17. C7×#63271 | C3×C4 | semidirect |
| 22. #11763964 | ΓL(1,𝔽8) | semidirect |
| 33. C72×C13 | C32×C4 | semidirect |
| 49. Dic91 | C3×ΓL(1,𝔽8) | semidirect |
| 55. #63271 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 56. #63271 | C4×ΓL(1,𝔽8) | semidirect |
| 75. #3862 | Dic13⋊C3 | semidirect |
| 84. C7×C13 | C3×ΓL(1,𝔽8)⋊C4 | semidirect |
| 85. C7×C13 | C3×C4×ΓL(1,𝔽8) | semidirect |
| 101. C72 | C3×Dic13⋊C3 | semidirect |
| 132. C13 | ΓL(1,𝔽8)×ΓL(1,𝔽8)⋊C4 | semidirect |
| 139. C7 | ΓL(1,𝔽8)×Dic13⋊C3 | semidirect |
| 140. C7 | ΓL(1,𝔽8)⋊(Dic13⋊C3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153212 | 2 |
| #21439556 | 3 |
| #21439542 | 3 |
| #21439532 | 3 |
| C7×#11763964 | 3 |
| ΓL(1,𝔽8)⋊(Dic13⋊C3) | 7 |
| ΓL(1,𝔽8)×Dic13⋊C3 | 7 |
| ΓL(1,𝔽8)×ΓL(1,𝔽8)⋊C4 | 13 |