Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
348 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 181 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. #22581082 | C2 | semidirect |
| 3. #22581080 | C2 | semidirect |
| 33. C2×C139⋊C8 | Q8 | semidirect |
| 83. C139 | #2961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581506 | 2 |
| #22581082 | 2 |
| #22581080 | 2 |
| #22580979 | 2 |
| #22580976 | 2 |
| #22580911 | 2 |
| #22580909 | 2 |
| C2×#17984752 | 2 |
| #424×C139 | 2 |
| #2961 | 139 |