Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
482 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 155 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. #20273467 | C2 | semidirect |
| 4. #20272553 | C2 | semidirect |
| 42. #100×C53 | C8 | semidirect |
| 61. M16×C53 | C2×C8 | semidirect |
| 149. C53 | #8835 | semidirect |
| 167. #100 | #88322 | semidirect |
| 191. M16 | C2×#88322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283739 | 2 |
| #20275510 | 2 |
| #20273467 | 2 |
| #20272553 | 2 |
| C4×#100×C53 | 2 |
| #8835 | 53 |