Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
584 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 584 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. #22598372 | C2 | semidirect |
| 3. #22589280 | C2 | semidirect |
| 4. #22586740 | C2 | semidirect |
| 5. C71×#1275 | C2 | semidirect |
| 84. C2×C8×C71 | SD16 | semidirect |
| 140. #1275 | D71 | semidirect |
| 141. C71 | #10034 | semidirect |
| 212. C2×C8 | #11765854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598786 | 2 |
| #22598372 | 2 |
| #22589280 | 2 |
| #22586740 | 2 |
| C71×#1275 | 2 |
| #10034 | 71 |