Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
420 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 102 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. #20290630 | C2 | semidirect |
| 3. #20290266 | C2 | semidirect |
| 5. #20289561 | C2 | semidirect |
| 6. #20289543 | C2 | semidirect |
| 91. M16×C53 | M16 | semidirect |
| 98. C42×C53 | M16 | semidirect |
| 216. C53 | #8842 | semidirect |
| 274. M16 | #11719936 | semidirect |
| 304. C42 | #11719936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291636 | 2 |
| #20290630 | 2 |
| #20290266 | 2 |
| #20290012 | 2 |
| #20289561 | 2 |
| #20289543 | 2 |
| #20274519 | 2 |
| #8842 | 53 |