Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
340 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 1. #22581720 | C2 | semidirect |
| 3. C2×#17984758 | C2 | semidirect |
| 4. #22580724 | C2 | semidirect |
| 5. #413×C139 | C2 | semidirect |
| 28. #14555769 | D4 | semidirect |
| 85. C139 | #1914 | semidirect |
| 89. #413 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581720 | 2 |
| #22581517 | 2 |
| C2×#17984758 | 2 |
| #22580724 | 2 |
| #413×C139 | 2 |
| #1914 | 139 |