Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
132 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 29 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, cosocle, hypocenter | C22×C72×C13 | C32 |
| LCS | G ▷ C22×C72×C13 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C13⋊#3862 | C3 | semidirect |
| 2. C72×A4×C13 | C3 | semidirect |
| 3. C22⋊(C13⋊#3862) | C3 | semidirect |
| 8. C22×C72×C13 | C32 | semidirect |
| 11. C13⋊#3862 | A4 | direct (N × H) |
| 17. C7×A4×C13 | ΓL(1,𝔽8) | semidirect |
| 18. C7×A4×C13 | ΓL(1,𝔽8) | semidirect |
| 23. C72×C13 | C3×A4 | semidirect |
| 25. C72×A4 | C13⋊C3 | semidirect |
| 32. C22×C7×C13 | C3×ΓL(1,𝔽8) | semidirect |
| 33. C22×C7×C13 | C3×ΓL(1,𝔽8) | semidirect |
| 44. C22×C72 | C3×C13⋊C3 | semidirect |
| 49. A4×C13 | #3862 | semidirect |
| 57. C7×C13 | A4×ΓL(1,𝔽8) | semidirect |
| 58. C7×C13 | A4×ΓL(1,𝔽8) | semidirect |
| 62. C7×A4 | #63270 | semidirect |
| 63. C7×A4 | #63271 | semidirect |
| 69. C22×C13 | C3×#3862 | semidirect |
| 70. C72 | A4×C13⋊C3 | semidirect |
| 78. C22×C7 | C3×#63270 | semidirect |
| 79. C22×C7 | C3×#63271 | semidirect |
| 91. C13 | A4×#3862 | semidirect |
| 94. A4 | C13⋊#3862 | direct (N × H) |
| 97. C7 | A4×#63270 | semidirect |
| 98. C7 | A4×#63271 | semidirect |
| 100. C22 | C3×C13⋊#3862 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13⋊#3862 | 3 |
| C72×A4×C13 | 3 |
| C22⋊(C13⋊#3862) | 3 |
| C3×C13⋊#3862 | 4 |
| A4×#63271 | 7 |
| A4×#63270 | 7 |
| A4×#3862 | 13 |