Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
260 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 260 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×#17984781 | C2 | semidirect |
| 3. #22580990 | C2 | semidirect |
| 4. #22580755 | C2 | semidirect |
| 5. #22580754 | C2 | semidirect |
| 6. #22580753 | C2 | semidirect |
| 7. #357×C139 | C2 | semidirect |
| 12. D8×D139 | C4 | semidirect |
| 16. C2×C139⋊C16 | C22 | semidirect |
| 17. #17984776 | C22 | semidirect |
| 20. C2×C16×C139 | C22 | semidirect |
| 21. #107×C139 | C22 | semidirect |
| 86. C139 | #2140 | semidirect |
| 94. #357 | D139 | semidirect |
| 105. C2×C16 | C2×D139 | semidirect |
| 107. #107 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D139 | 2 |
| C2×#17984781 | 2 |
| #22580990 | 2 |
| #22580755 | 2 |
| #22580754 | 2 |
| #22580753 | 2 |
| #357×C139 | 2 |
| #2140 | 139 |