Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
226 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C227 | #447 |
| commutator, Frattini, cosocle | C2×C8 | C23×C227 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C227 ◁ C2×C4×C227 ◁ C2×M16×C227 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #575×C227 | C2 | semidirect |
| 2. #509×C227 | C2 | semidirect |
| 3. #469×C227 | C2 | semidirect |
| 4. #360×C227 | C2 | semidirect |
| 5. #349×C227 | C2 | semidirect |
| 11. C2×D8×C227 | C22 | semidirect |
| 16. M32×C227 | C22 | semidirect |
| 17. #106×C227 | C22 | semidirect |
| 31. Q16×C227 | D4 | semidirect |
| 36. D8×C227 | D4 | semidirect |
| 83. C227 | #2190 | direct (N × H) |
| 84. #2190 | C227 | direct (N × H) |
| 85. #575 | C2×C227 | semidirect |
| 86. #509 | C2×C227 | semidirect |
| 87. #469 | C2×C227 | semidirect |
| 88. #360 | C2×C227 | semidirect |
| 89. #349 | C2×C227 | semidirect |
| 95. C2×D8 | C22×C227 | semidirect |
| 100. M32 | C22×C227 | semidirect |
| 101. #106 | C22×C227 | semidirect |
| 115. Q16 | D4×C227 | semidirect |
| 120. D8 | D4×C227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #575×C227 | 2 |
| #509×C227 | 2 |
| #469×C227 | 2 |
| #360×C227 | 2 |
| #349×C227 | 2 |
| #2190 | 227 |