Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
238 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 95 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. #19136497 | C2 | semidirect |
| 4. #19132573 | C2 | semidirect |
| 6. C8×C43⋊C16 | C2 | semidirect |
| 7. C43×#1367 | C2 | semidirect |
| 60. #10621873 | C16 | semidirect |
| 67. C43⋊C16 | SD16 | semidirect |
| 80. Dic86 | C2×C16 | semidirect |
| 84. C8×C43 | C2×C16 | semidirect |
| 105. #1367 | D43 | semidirect |
| 128. C43 | C16×SD16 | semidirect |
| 192. C8 | C16×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136497 | 2 |
| #19136414 | 2 |
| C8×#10621873 | 2 |
| #19132573 | 2 |
| #19132549 | 2 |
| C8×C43⋊C16 | 2 |
| C43×#1367 | 2 |
| C16×SD16 | 43 |