Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
264 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 97 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×C4⋊(C139⋊C8) | C2 | semidirect |
| 3. #22580685 | C2 | semidirect |
| 4. #22580682 | C2 | semidirect |
| 5. #431×C139 | C2 | semidirect |
| 24. #14555785 | C8 | semidirect |
| 53. Dic278 | C2×C8 | semidirect |
| 55. D556 | C2×C8 | semidirect |
| 101. C139 | #1477 | semidirect |
| 104. #431 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14555785 | 2 |
| C2×C4⋊(C139⋊C8) | 2 |
| #22580685 | 2 |
| #22580682 | 2 |
| #431×C139 | 2 |
| #1477 | 139 |