Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
306 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 306 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 |
|---|---|---|
| 2. C2×#17984770 | C2 | semidirect |
| 3. #22580955 | C2 | semidirect |
| 4. #22580954 | C2 | semidirect |
| 5. #22580823 | C2 | semidirect |
| 6. #22580721 | C2 | semidirect |
| 7. C2×#104×C139 | C2 | semidirect |
| 63. C42×C139 | D4 | semidirect |
| 128. C139 | #2039 | semidirect |
| 132. C2×#104 | D139 | semidirect |
| 192. C42 | C22⋊D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581531 | 2 |
| C2×#17984770 | 2 |
| #22580955 | 2 |
| #22580954 | 2 |
| #22580823 | 2 |
| #22580721 | 2 |
| C2×#104×C139 | 2 |
| #2039 | 139 |