Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1118 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 1118 conjugacy classes of subgroups — too many to draw. Only its 207 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20243681 | C2 | semidirect |
| 2. #20241706 | C2 | semidirect |
| 4. C23×C47⋊C8 | C22 | semidirect |
| 6. C2×C22⋊(C47⋊C8) | C22 | semidirect |
| 23. H(5,𝔽2)×C47 | C8 | semidirect |
| 102. C23×C47 | C22⋊C8 | semidirect |
| 125. C2×C4×C47 | C22⋊C8 | semidirect |
| 172. C47 | #8316 | semidirect |
| 174. H(5,𝔽2) | C47⋊C8 | semidirect |
| 258. C23 | C22⋊(C47⋊C8) | semidirect |
| 281. C2×C4 | C22⋊(C47⋊C8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20243681 | 2 |
| #20241706 | 2 |
| C4×H(5,𝔽2)×C47 | 2 |
| #8316 | 47 |