Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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. Q8×Dic278 | C2 | semidirect |
| 5. #22580701 | C2 | semidirect |
| 6. #22580685 | C2 | semidirect |
| 7. Q8⋊C8×C139 | C2 | semidirect |
| 54. Dic278 | SD16 | semidirect |
| 65. Q8×C139 | SD16 | semidirect |
| 91. C139 | #1623 | semidirect |
| 99. Q8⋊C8 | D139 | semidirect |
| 148. Q8 | #14555774 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic278 | 2 |
| #22581326 | 2 |
| #22581154 | 2 |
| #22581153 | 2 |
| #22580701 | 2 |
| #22580685 | 2 |
| Q8⋊C8×C139 | 2 |
| #1623 | 139 |