Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
374 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 374 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 |
| 3. #22587112 | C2 | semidirect |
| 4. #22587090 | C2 | semidirect |
| 7. C71×#1292 | C2 | semidirect |
| 164. #1292 | D71 | semidirect |
| 165. C71 | #10607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589179 | 2 |
| #22589113 | 2 |
| #22587112 | 2 |
| #22587090 | 2 |
| #22587009 | 2 |
| C2×#17985742 | 2 |
| C71×#1292 | 2 |
| #10607 | 71 |