Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
176 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 79. C139 | #2090 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22580996 | 2 |
| C2×#17984773 | 2 |
| #22580980 | 2 |
| #22580722 | 2 |
| #22580721 | 2 |
| #22580717 | 2 |
| #428×C139 | 2 |
| #2090 | 139 |