Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
834 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 179 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×#14583330 | C2 | semidirect |
| 2. #19145024 | C2 | semidirect |
| 3. #19145022 | C2 | semidirect |
| 4. #19136855 | C2 | semidirect |
| 5. #19136851 | C2 | semidirect |
| 6. #19136847 | C2 | semidirect |
| 7. #19136844 | C2 | semidirect |
| 8. C4×C16×D43 | C2 | semidirect |
| 9. C43×#2248 | C2 | semidirect |
| 65. C16×D43 | D4 | semidirect |
| 160. C4×C43 | #508 | semidirect |
| 171. #2248 | D43 | semidirect |
| 206. C43 | #33713 | semidirect |
| 333. C4 | #14583330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583330 | 2 |
| #19145024 | 2 |
| #19145022 | 2 |
| #19136855 | 2 |
| #19136851 | 2 |
| #19136847 | 2 |
| #19136844 | 2 |
| C4×C16×D43 | 2 |
| C43×#2248 | 2 |
| #33713 | 43 |