Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
362 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
| 73. Q16×C43 | M16 | semidirect |
| 97. Dic172 | M16 | semidirect |
| 155. #1334 | D43 | semidirect |
| 179. C43 | #11664 | semidirect |
| 229. Q16 | #10621872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q16×D43 | 2 |
| #19136396 | 2 |
| #19133349 | 2 |
| #19132566 | 2 |
| #19132565 | 2 |
| #19132564 | 2 |
| C43×#1334 | 2 |
| #11664 | 43 |