Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
344 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 344 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. #22580977 | C2 | semidirect |
| 3. #22580696 | C2 | semidirect |
| 4. #431×C139 | C2 | semidirect |
| 14. C4⋊(C139⋊C8) | C22 | semidirect |
| 16. C4⋊C8×C139 | C22 | semidirect |
| 84. C139 | #1545 | semidirect |
| 87. #431 | D139 | semidirect |
| 101. C4⋊C8 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984839 | 2 |
| #22580977 | 2 |
| #22580696 | 2 |
| #431×C139 | 2 |
| #1545 | 139 |