Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#17984870 | C2 | semidirect |
| 2. #22581522 | C2 | semidirect |
| 3. C2×#17984839 | C2 | semidirect |
| 4. C2×#17984770 | C2 | semidirect |
| 5. #22580957 | C2 | semidirect |
| 6. C2×#17984758 | C2 | semidirect |
| 7. #339×C139 | C2 | semidirect |
| 35. C2×Dic278 | D4 | semidirect |
| 50. C2×D556 | D4 | semidirect |
| 51. C2×D556 | D4 | semidirect |
| 63. M16×C139 | D4 | semidirect |
| 65. C4⋊C4×C139 | D4 | semidirect |
| 69. C42×C139 | D4 | semidirect |
| 138. C139 | #2002 | semidirect |
| 146. #339 | D139 | semidirect |
| 200. M16 | D556 | semidirect |
| 203. C4⋊C4 | D556 | semidirect |
| 208. C42 | D556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984870 | 2 |
| #22581522 | 2 |
| C2×#17984839 | 2 |
| C2×#17984770 | 2 |
| #22580957 | 2 |
| C2×#17984758 | 2 |
| #339×C139 | 2 |
| #2002 | 139 |