Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
664 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 151 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×Q32×D43 | C2 | semidirect |
| 3. #19136683 | C2 | semidirect |
| 4. #19136642 | C2 | semidirect |
| 5. #19136527 | C2 | semidirect |
| 6. C4×Dic344 | C2 | semidirect |
| 8. C43×#2247 | C2 | semidirect |
| 41. Dic344 | D4 | semidirect |
| 100. D172 | Q32 | semidirect |
| 115. C2×D43 | C2×Q32 | semidirect |
| 118. C4×C43 | C2×Q32 | semidirect |
| 126. #2247 | D43 | semidirect |
| 156. C43 | D4×Q32 | semidirect |
| 248. C4 | Q32×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q32×D43 | 2 |
| #19146345 | 2 |
| #19136683 | 2 |
| #19136642 | 2 |
| #19136527 | 2 |
| C4×Dic344 | 2 |
| C16×D172 | 2 |
| C43×#2247 | 2 |
| D4×Q32 | 43 |