Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
444 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. C2×#14582722 | C2 | semidirect |
| 3. C2×#14582713 | C2 | semidirect |
| 4. C2×#14582710 | C2 | semidirect |
| 5. #19135488 | C2 | semidirect |
| 6. #19135471 | C2 | semidirect |
| 7. C2×C43×#347 | C2 | semidirect |
| 12. C2×#13063270 | C4 | semidirect |
| 13. C2×D688 | C4 | semidirect |
| 111. C16×C43 | C22⋊C4 | semidirect |
| 171. C2×#347 | D43 | semidirect |
| 199. C43 | #13249 | semidirect |
| 284. C16 | (C2×D43)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583337 | 2 |
| C2×#14582722 | 2 |
| C2×#14582713 | 2 |
| C2×#14582710 | 2 |
| #19135488 | 2 |
| #19135471 | 2 |
| C2×C43×#347 | 2 |
| #13249 | 43 |