Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
474 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #20244304 | C2 | semidirect |
| 5. #20241496 | C2 | semidirect |
| 6. #20241476 | C2 | semidirect |
| 7. C2×C47×#358 | C2 | semidirect |
| 11. #15689564 | C4 | semidirect |
| 47. #13093964 | C2×C4 | semidirect |
| 64. C2×Q16×C47 | C2×C4 | semidirect |
| 179. C2×#358 | D47 | semidirect |
| 209. C47 | #13023 | semidirect |
| 222. C2×Q16 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689564 | 2 |
| #20252262 | 2 |
| C2×#15688931 | 2 |
| #20244304 | 2 |
| #20241496 | 2 |
| #20241476 | 2 |
| C2×C47×#358 | 2 |
| #13023 | 47 |