Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
386 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22589113 | C2 | semidirect |
| 4. C2×#17985748 | C2 | semidirect |
| 6. #22586189 | C2 | semidirect |
| 7. C71×#1549 | C2 | semidirect |
| 173. #1549 | D71 | semidirect |
| 178. C71 | #10551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598736 | 2 |
| #22589113 | 2 |
| #22587018 | 2 |
| C2×#17985748 | 2 |
| #22586740 | 2 |
| #22586189 | 2 |
| C71×#1549 | 2 |
| #10551 | 71 |