Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
176 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 61 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. #29504850 | C2 | semidirect |
| 3. #29504849 | C2 | semidirect |
| 4. #29504522 | C2 | semidirect |
| 5. #29504501 | C2 | semidirect |
| 6. #29504494 | C2 | semidirect |
| 7. D4⋊C8×C239 | C2 | semidirect |
| 52. C239⋊C8 | M16 | semidirect |
| 83. C239 | #1594 | semidirect |
| 90. D4⋊C8 | D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16838533 | 2 |
| #29504850 | 2 |
| #29504849 | 2 |
| #29504522 | 2 |
| #29504501 | 2 |
| #29504494 | 2 |
| D4⋊C8×C239 | 2 |
| #1594 | 239 |