Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
226 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 71 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. #19133510 | C2 | semidirect |
| 3. #19132661 | C2 | semidirect |
| 4. #19132563 | C2 | semidirect |
| 5. C43×#1313 | C2 | semidirect |
| 43. C16×C43 | M16 | semidirect |
| 70. #1313 | D43 | semidirect |
| 84. C43 | #12089 | semidirect |
| 112. C16 | #10621872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136472 | 2 |
| #19133510 | 2 |
| #19132661 | 2 |
| #19132563 | 2 |
| C43×#1313 | 2 |
| #12089 | 43 |