Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
398 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
| 31. Q16×D53 | C8 | semidirect |
| 74. Q16×C53 | C2×C8 | semidirect |
| 98. Dic212 | C2×C8 | semidirect |
| 156. #1334 | D53 | direct (N × H) |
| 160. D53 | #1334 | direct (N × H) |
| 180. C53 | C2×#1334 | semidirect |
| 231. Q16 | C8×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q16×D53 | 2 |
| #346×D53 | 2 |
| #334×D53 | 2 |
| #20272686 | 2 |
| #20272685 | 2 |
| #20272684 | 2 |
| C53×#1334 | 2 |
| C2×#1334 | 53 |