Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
224 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 3. #19132666 | C2 | semidirect |
| 4. #19132559 | C2 | semidirect |
| 6. #19132513 | C2 | semidirect |
| 7. C8×Q16×C43 | C2 | semidirect |
| 48. Q16×C43 | M16 | semidirect |
| 104. C8×Q16 | D43 | semidirect |
| 128. C43 | #12075 | semidirect |
| 154. Q16 | #10621872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13063268 | 2 |
| #19133481 | 2 |
| #19132666 | 2 |
| #19132559 | 2 |
| #19132555 | 2 |
| #19132513 | 2 |
| C8×Q16×C43 | 2 |
| #12075 | 43 |