Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
284 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 128 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. #20289630 | C2 | semidirect |
| 4. #20289630 | C2 | semidirect |
| 5. #20289627 | C2 | semidirect |
| 6. C8×#11719910 | C2 | semidirect |
| 64. #11719910 | M16 | semidirect |
| 81. #88322 | M32 | semidirect |
| 122. C53 | #11409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291074 | 2 |
| C4×#13133292 | 2 |
| #20289630 | 2 |
| #20289627 | 2 |
| C8×#11719910 | 2 |
| #20272994 | 2 |
| #11409 | 53 |