Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
528 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22598886 | C2 | semidirect |
| 4. #22589262 | C2 | semidirect |
| 6. #22586840 | C2 | semidirect |
| 7. C71×#1283 | C2 | semidirect |
| 117. M16×C71 | SD16 | semidirect |
| 197. #1283 | D71 | semidirect |
| 198. C71 | #10201 | semidirect |
| 289. M16 | #11765854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599657 | 2 |
| #22599470 | 2 |
| #22598886 | 2 |
| #22589262 | 2 |
| #22589259 | 2 |
| #22586840 | 2 |
| C71×#1283 | 2 |
| #10201 | 71 |