Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
534 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 167 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. #22590560 | C2 | semidirect |
| 4. #22590113 | C2 | semidirect |
| 5. C2×#17985816 | C2 | semidirect |
| 132. C71 | #33658 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597995 | 2 |
| #22596951 | 2 |
| #22590560 | 2 |
| #22590113 | 2 |
| C2×#17985816 | 2 |
| C71×#2115 | 2 |
| #33658 | 71 |