Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
362 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #20272686 | C2 | semidirect |
| 5. #20272685 | C2 | semidirect |
| 6. #20272684 | C2 | semidirect |
| 7. C53×#1334 | C2 | semidirect |
| 73. Q16×C53 | M16 | semidirect |
| 97. Dic212 | M16 | semidirect |
| 155. #1334 | D53 | semidirect |
| 179. C53 | #11664 | semidirect |
| 229. Q16 | #11719912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q16×D53 | 2 |
| #20276516 | 2 |
| #20273469 | 2 |
| #20272686 | 2 |
| #20272685 | 2 |
| #20272684 | 2 |
| C53×#1334 | 2 |
| #11664 | 53 |