Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
3262 conjugacy classes of subgroups; only the 987 normal subgroups are shown.
This group has 3262 conjugacy classes of subgroups — too many to draw. Only its 987 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 |
|---|---|---|
| 3. C2×#15689502 | C2 | direct (N × H) |
| 13. #15689502 | C22 | direct (N × H) |
| 50. C22×C4×C47 | Q16 | semidirect |
| 76. C2×C4×C47 | C2×Q16 | semidirect |
| 87. C22×C47 | #494 | semidirect |
| 93. C4×C47 | C22×Q16 | semidirect |
| 101. C2×C47 | C2×#494 | semidirect |
| 118. C47 | C22×#494 | semidirect |
| 155. C22×C4 | #10625337 | semidirect |
| 179. C2×C4 | C2×#10625337 | semidirect |
| 185. C22 | #15689502 | direct (N × H) |
| 192. C4 | C22×#10625337 | semidirect |
| 194. C2 | C2×#15689502 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#10625337 | 2 |
| C22×#13094024 | 2 |
| C2×#15689502 | 2 |
| C22×C4×C47⋊C8 | 2 |
| C22×C4⋊Q8×C47 | 2 |
| C22×#494 | 47 |