Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
488 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 488 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 |
|---|---|---|
| 3. C2×Q8⋊#88324 | C2 | semidirect |
| 4. #20289958 | C2 | semidirect |
| 5. #20289561 | C2 | semidirect |
| 6. #20289548 | C2 | semidirect |
| 93. C2×Q8×C53 | M16 | semidirect |
| 115. M16×C53 | M16 | semidirect |
| 246. C53 | #9098 | semidirect |
| 306. C2×Q8 | #11719940 | semidirect |
| 324. M16 | #11719940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291524 | 2 |
| #20290010 | 2 |
| C2×Q8⋊#88324 | 2 |
| #20289958 | 2 |
| #20289561 | 2 |
| #20289548 | 2 |
| #137×Dic53 | 2 |
| #9098 | 53 |