Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
224 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 81 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×Dic172 | C2 | semidirect |
| 3. #19132668 | C2 | semidirect |
| 4. #19132558 | C2 | semidirect |
| 6. #19132513 | C2 | semidirect |
| 64. Dic172 | M16 | semidirect |
| 85. C8×C43 | SD32 | semidirect |
| 128. C43 | #12071 | semidirect |
| 192. C8 | #13063269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13063269 | 2 |
| C8×Dic172 | 2 |
| #19132668 | 2 |
| #19132558 | 2 |
| #19132556 | 2 |
| #19132513 | 2 |
| C43×#1589 | 2 |
| #12071 | 43 |