Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
474 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 84 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×#16811536 | C2 | semidirect |
| 4. #20290877 | C2 | semidirect |
| 5. #20289790 | C2 | semidirect |
| 6. #20289771 | C2 | semidirect |
| 24. #16811066 | C4 | semidirect |
| 26. #16811064 | C4 | semidirect |
| 27. #16811063 | C4 | semidirect |
| 32. C53×#510 | C4 | semidirect |
| 63. C2×Dic212 | C2×C4 | semidirect |
| 79. #13133157 | C2×C4 | semidirect |
| 83. C2×Q16×C53 | C2×C4 | semidirect |
| 86. M32×C53 | C2×C4 | semidirect |
| 235. #510 | #6157 | semidirect |
| 252. C53 | #13023 | semidirect |
| 268. C2×Q16 | C2×#6157 | semidirect |
| 291. M32 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291477 | 2 |
| D53⋊#359 | 2 |
| C2×#16811536 | 2 |
| #20290877 | 2 |
| #20289790 | 2 |
| #20289771 | 2 |
| #510×D53 | 2 |
| #13023 | 53 |