Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
436 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 141 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×#17984764 | C2 | semidirect |
| 3. #22580823 | C2 | semidirect |
| 4. C2×C4×C8×C139 | C2 | semidirect |
| 8. #17984839 | C4 | semidirect |
| 30. C2×C8×C139 | D4 | semidirect |
| 62. C4×C139 | #102 | semidirect |
| 72. C139 | #1957 | semidirect |
| 76. C2×C4×C8 | D139 | semidirect |
| 101. C2×C8 | D556 | semidirect |
| 136. C4 | #17984764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984839 | 2 |
| C2×#17984764 | 2 |
| #22580823 | 2 |
| C2×C4×C8×C139 | 2 |
| #1957 | 139 |