Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1738 conjugacy classes of subgroups; only the 587 normal subgroups are shown.
This group has 1738 conjugacy classes of subgroups — too many to draw. Only its 587 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. #22594305 | C2 | semidirect |
| 2. #22594300 | C2 | semidirect |
| 3. #22594293 | C2 | semidirect |
| 4. #22591638 | C2 | semidirect |
| 6. #22590823 | C2 | semidirect |
| 7. C2×#376×C71 | C2 | semidirect |
| 108. C2×#376 | D71 | semidirect |
| 109. C71 | #34639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22594305 | 2 |
| #22594300 | 2 |
| #22594293 | 2 |
| #22591638 | 2 |
| #22590830 | 2 |
| #22590823 | 2 |
| C2×#376×C71 | 2 |
| #34639 | 71 |