Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20276516 | C2 | semidirect |
| 3. #20273469 | C2 | semidirect |
| 4. #20272685 | C2 | semidirect |
| 5. #20272683 | C2 | semidirect |
| 6. #20272681 | C2 | semidirect |
| 7. C53×#1334 | C2 | semidirect |
| 74. Q16×C53 | M16 | semidirect |
| 97. D424 | M16 | semidirect |
| 156. #1334 | D53 | semidirect |
| 183. C53 | #11666 | semidirect |
| 231. Q16 | #11719912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133240 | 2 |
| #20276516 | 2 |
| #20273469 | 2 |
| #20272685 | 2 |
| #20272683 | 2 |
| #20272681 | 2 |
| C53×#1334 | 2 |
| #11666 | 53 |