Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
246 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 77 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. #22581010 | C2 | semidirect |
| 3. #22580685 | C2 | semidirect |
| 4. #22580682 | C2 | semidirect |
| 5. #431×C139 | C2 | semidirect |
| 97. C139 | #1488 | semidirect |
| 101. #431 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14555785 | 2 |
| #22581010 | 2 |
| #22580685 | 2 |
| #22580682 | 2 |
| #431×C139 | 2 |
| #1488 | 139 |