Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
216 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 79 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. #19136433 | C2 | semidirect |
| 3. #19132670 | C2 | semidirect |
| 4. #19132568 | C2 | semidirect |
| 5. #19132567 | C2 | semidirect |
| 6. C16×C43⋊C8 | C2 | semidirect |
| 7. C43×#2170 | C2 | semidirect |
| 25. #13063271 | C8 | semidirect |
| 26. #13063269 | C8 | semidirect |
| 27. #13063268 | C8 | semidirect |
| 28. #13063266 | C8 | semidirect |
| 101. #2170 | D43 | semidirect |
| 125. C43 | #12046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136474 | 2 |
| #19136433 | 2 |
| #19132670 | 2 |
| #19132568 | 2 |
| #19132567 | 2 |
| C16×C43⋊C8 | 2 |
| C43×#2170 | 2 |
| #12046 | 43 |