Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
398 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 111 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. #19132566 | C2 | semidirect |
| 5. #19132565 | C2 | semidirect |
| 6. #19132564 | C2 | semidirect |
| 7. C43×#1334 | C2 | semidirect |
| 31. Q16×D43 | C8 | semidirect |
| 74. Q16×C43 | C2×C8 | semidirect |
| 98. Dic172 | C2×C8 | semidirect |
| 156. #1334 | D43 | direct (N × H) |
| 160. D43 | #1334 | direct (N × H) |
| 180. C43 | C2×#1334 | semidirect |
| 231. Q16 | C8×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q16×D43 | 2 |
| #346×D43 | 2 |
| #334×D43 | 2 |
| #19132566 | 2 |
| #19132565 | 2 |
| #19132564 | 2 |
| C43×#1334 | 2 |
| C2×#1334 | 43 |