Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
456 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 3. #22581061 | C2 | semidirect |
| 4. #22581060 | C2 | semidirect |
| 5. #22581059 | C2 | semidirect |
| 6. C4×#14555775 | C2 | semidirect |
| 7. #22581045 | C2 | semidirect |
| 11. #441×C139 | C2 | semidirect |
| 15. Q16×D139 | C4 | semidirect |
| 108. C139 | #2950 | semidirect |
| 115. #441 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D139 | 2 |
| #22581429 | 2 |
| #22581061 | 2 |
| #22581060 | 2 |
| #22581059 | 2 |
| C4×#14555775 | 2 |
| #22581045 | 2 |
| #22580988 | 2 |
| #22580960 | 2 |
| #22580910 | 2 |
| #441×C139 | 2 |
| #2950 | 139 |