Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
176 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 176 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 |
|---|---|---|
| 1. #26038786 | C2 | semidirect |
| 2. #26038729 | C2 | semidirect |
| 4. #26038190 | C2 | semidirect |
| 5. #26038187 | C2 | semidirect |
| 6. #26038182 | C2 | semidirect |
| 7. C8×D4×C179 | C2 | semidirect |
| 82. C179 | #1677 | semidirect |
| 87. C8×D4 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26038786 | 2 |
| #26038729 | 2 |
| #26038634 | 2 |
| #26038190 | 2 |
| #26038187 | 2 |
| #26038182 | 2 |
| C8×D4×C179 | 2 |
| #1677 | 179 |