Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
798 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 211 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. #19145155 | C2 | semidirect |
| 3. #19134229 | C2 | semidirect |
| 4. #19134224 | C2 | semidirect |
| 5. #19134218 | C2 | semidirect |
| 6. C2×#14582620 | C2 | semidirect |
| 7. C43×#3160 | C2 | semidirect |
| 67. C2×C8×C43 | SD16 | semidirect |
| 118. #3160 | D43 | semidirect |
| 149. C43 | #19608 | semidirect |
| 194. C2×C8 | #10621884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145155 | 2 |
| #19145023 | 2 |
| #19134229 | 2 |
| #19134224 | 2 |
| #19134218 | 2 |
| C2×#14582620 | 2 |
| C43×#3160 | 2 |
| #19608 | 43 |