Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
360 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 145 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. #22581355 | C2 | semidirect |
| 3. #22581354 | C2 | semidirect |
| 4. #22581353 | C2 | semidirect |
| 5. #22581352 | C2 | semidirect |
| 9. #499×C139 | C2 | semidirect |
| 75. D139 | #499 | direct (N × H) |
| 76. C139 | C2×#499 | semidirect |
| 83. #499 | D139 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #125×D139 | 2 |
| #22581355 | 2 |
| #22581354 | 2 |
| #22581353 | 2 |
| #22581352 | 2 |
| #107×D139 | 2 |
| #106×D139 | 2 |
| C4×C8×D139 | 2 |
| #499×C139 | 2 |
| C2×#499 | 139 |