Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1502 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1502 conjugacy classes of subgroups — too many to draw. Only its 331 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×#14583293 | C2 | semidirect |
| 2. C2×#14583288 | C2 | semidirect |
| 3. C2×#14583283 | C2 | semidirect |
| 4. #19142952 | C2 | semidirect |
| 5. C4×#97×C43 | C2 | semidirect |
| 42. #97×C43 | D4 | semidirect |
| 43. C4×C8×C43 | D4 | semidirect |
| 106. C4×#97 | D43 | semidirect |
| 125. C43 | #33306 | semidirect |
| 148. #97 | D172 | semidirect |
| 149. C4×C8 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583293 | 2 |
| C2×#14583288 | 2 |
| C2×#14583283 | 2 |
| #19142952 | 2 |
| C4×#97×C43 | 2 |
| #33306 | 43 |