Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
308 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26038716 | C2 | semidirect |
| 3. #26038641 | C2 | semidirect |
| 4. #26038183 | C2 | semidirect |
| 5. #26038168 | C2 | semidirect |
| 6. #26038168 | C2 | semidirect |
| 7. #486×C179 | C2 | semidirect |
| 17. C4⋊(C179⋊C8) | C22 | semidirect |
| 18. C4⋊(C179⋊C8) | C22 | semidirect |
| 21. C4⋊Q8×C179 | C22 | semidirect |
| 24. C4×C8×C179 | C22 | semidirect |
| 60. D716 | SD16 | semidirect |
| 109. C179 | #1639 | semidirect |
| 112. #486 | D179 | semidirect |
| 121. C4⋊Q8 | C2×D179 | semidirect |
| 134. C4×C8 | C2×D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26039074 | 2 |
| #26038716 | 2 |
| #26038641 | 2 |
| #26038183 | 2 |
| #26038168 | 2 |
| #486×C179 | 2 |
| #1639 | 179 |