Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
772 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#14583217 | C2 | semidirect |
| 3. C2×#14582634 | C2 | semidirect |
| 4. C2×#14582633 | C2 | semidirect |
| 5. #19132863 | C2 | semidirect |
| 6. #19132437 | C2 | semidirect |
| 7. C2×C43×#481 | C2 | semidirect |
| 51. C22⋊(C43⋊C8) | D4 | semidirect |
| 72. C2×C4⋊C4×C43 | D4 | semidirect |
| 77. C22⋊C8×C43 | D4 | semidirect |
| 238. C2×#481 | D43 | semidirect |
| 277. C43 | #9968 | semidirect |
| 307. C2×C4⋊C4 | C22⋊D43 | semidirect |
| 319. C22⋊C8 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583217 | 2 |
| #19140699 | 2 |
| C2×#14582634 | 2 |
| C2×#14582633 | 2 |
| #19132863 | 2 |
| #19132437 | 2 |
| C2×C43×#481 | 2 |
| #9968 | 43 |