Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×Q16×D181 | C2 | semidirect |
| 3. #26041659 | C2 | semidirect |
| 4. #26041521 | C2 | semidirect |
| 5. #26041489 | C2 | semidirect |
| 6. #26041436 | C2 | semidirect |
| 8. C4×Q16×C181 | C2 | semidirect |
| 48. Q16×C181 | D4 | semidirect |
| 59. D724 | Q16 | direct (N × H) |
| 78. C2×D181 | C2×Q16 | semidirect |
| 82. C4×C181 | C2×Q16 | semidirect |
| 91. C181 | D4×Q16 | semidirect |
| 99. C4×Q16 | D181 | semidirect |
| 132. Q16 | D724 | direct (N × H) |
| 176. C4 | Q16×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D181 | 2 |
| Q8×D724 | 2 |
| #26041659 | 2 |
| #26041521 | 2 |
| #26041489 | 2 |
| #26041436 | 2 |
| C8×D724 | 2 |
| C4×Q16×C181 | 2 |
| D4×Q16 | 181 |