Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
528 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22598882 | C2 | semidirect |
| 3. #22589264 | C2 | semidirect |
| 5. #22586840 | C2 | semidirect |
| 6. #22586189 | C2 | semidirect |
| 82. #11765849 | SD16 | semidirect |
| 198. C71 | #10201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599656 | 2 |
| #22598882 | 2 |
| #22589264 | 2 |
| #22589260 | 2 |
| #22586840 | 2 |
| #22586189 | 2 |
| C71×#3227 | 2 |
| #10201 | 71 |