Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 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. #22589280 | C2 | semidirect |
| 5. #22586770 | C2 | semidirect |
| 6. #22586236 | C2 | semidirect |
| 7. C71×#1281 | C2 | semidirect |
| 115. C2×C8×C71 | SD16 | semidirect |
| 192. #1281 | D71 | semidirect |
| 193. C71 | #9047 | semidirect |
| 291. C2×C8 | #11765854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598372 | 2 |
| #22597059 | 2 |
| #22589280 | 2 |
| #22586987 | 2 |
| #22586770 | 2 |
| #22586236 | 2 |
| C71×#1281 | 2 |
| #9047 | 71 |