Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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. #22581673 | C2 | semidirect |
| 2. #22581299 | C2 | semidirect |
| 3. #22581150 | C2 | semidirect |
| 4. #22580700 | C2 | semidirect |
| 5. #22580683 | C2 | semidirect |
| 6. D4⋊(C139⋊C8) | C2 | semidirect |
| 95. C139 | #1628 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581673 | 2 |
| #22581299 | 2 |
| #22581150 | 2 |
| #22580700 | 2 |
| #22580683 | 2 |
| D4⋊(C139⋊C8) | 2 |
| #459×C139 | 2 |
| #1628 | 139 |