Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1618 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1618 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×#14583288 | C2 | semidirect |
| 2. C2×#14583283 | C2 | semidirect |
| 3. C2×#14583276 | C2 | semidirect |
| 4. #19140701 | C2 | semidirect |
| 5. C43×#1726 | C2 | semidirect |
| 37. #97×C43 | D4 | semidirect |
| 38. C4×C8×C43 | D4 | semidirect |
| 93. #1726 | D43 | semidirect |
| 110. C43 | #33308 | semidirect |
| 129. #97 | D172 | semidirect |
| 130. C4×C8 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583288 | 2 |
| C2×#14583283 | 2 |
| C2×#14583276 | 2 |
| #19140701 | 2 |
| C43×#1726 | 2 |
| #33308 | 43 |