Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
330 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 330 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 |
|---|---|---|
| 1. #22590597 | C2 | semidirect |
| 2. #22590595 | C2 | semidirect |
| 3. #22590592 | C2 | semidirect |
| 5. #22587946 | C2 | semidirect |
| 6. C8×C71⋊C16 | C2 | semidirect |
| 7. C71×#1709 | C2 | semidirect |
| 104. #1709 | D71 | semidirect |
| 106. C71 | #12518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590597 | 2 |
| #22590595 | 2 |
| #22590592 | 2 |
| #22590589 | 2 |
| #22587946 | 2 |
| C8×C71⋊C16 | 2 |
| C71×#1709 | 2 |
| #12518 | 71 |