Finite Group DatabasebetaFinite Group DatabasebetaOrder 33472.
124 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 53 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×#22552624 | C2 | semidirect |
| 2. C2×C8×D523 | C2 | semidirect |
| 4. C4⋊(C523⋊C8) | C2 | semidirect |
| 5. (C2×D523)⋊C8 | C2 | semidirect |
| 6. (C2×D523)⋊C8 | C2 | semidirect |
| 7. #97×C523 | C2 | semidirect |
| 36. C8×C523 | D4 | semidirect |
| 43. C2×D523 | M16 | semidirect |
| 55. C523 | #435 | semidirect |
| 63. #97 | D523 | semidirect |
| 92. C8 | D2092 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22552624 | 2 |
| C2×C8×D523 | 2 |
| C4×D2092 | 2 |
| C4⋊(C523⋊C8) | 2 |
| (C2×D523)⋊C8 | 2 |
| #97×C523 | 2 |
| #435 | 523 |