Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
240 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 2. C8×D344 | C2 | semidirect |
| 3. #19132668 | C2 | semidirect |
| 4. #19132556 | C2 | semidirect |
| 5. #19132555 | C2 | semidirect |
| 6. #19132513 | C2 | semidirect |
| 7. C43×#1589 | C2 | semidirect |
| 64. D344 | M16 | semidirect |
| 108. #1589 | D43 | semidirect |
| 134. C43 | #12073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13063266 | 2 |
| C8×D344 | 2 |
| #19132668 | 2 |
| #19132556 | 2 |
| #19132555 | 2 |
| #19132513 | 2 |
| C43×#1589 | 2 |
| #12073 | 43 |