Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
242 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #19132669 | C2 | semidirect |
| 5. #19132668 | C2 | semidirect |
| 6. #19132666 | C2 | semidirect |
| 7. C43×#1371 | C2 | semidirect |
| 28. #13063264 | C8 | semidirect |
| 64. C16×C43 | C2×C8 | semidirect |
| 66. C43⋊C16 | C2×C8 | semidirect |
| 107. #1371 | D43 | semidirect |
| 127. C43 | #12009 | semidirect |
| 171. C16 | C8×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13063264 | 2 |
| #19133342 | 2 |
| #335×D43 | 2 |
| #19132669 | 2 |
| #19132668 | 2 |
| #19132666 | 2 |
| C43×#1371 | 2 |
| #12009 | 43 |